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TrigonometryQuestion and Answers: Page 1

Question Number 206787 Answers: 0 Comments: 1

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Question Number 206618 Answers: 2 Comments: 0

If A = sin^4 θ + cos^4 θ then select the correct option: i) 0 < A < (1/2) ii) 1 < A < (3/2) iii) (1/2) ≤ A ≤ 1 iv) (3/2) ≤ A ≤ 2

$$\mathrm{If}\:\mathrm{A}\:=\:\mathrm{sin}^{\mathrm{4}} \theta\:+\:\mathrm{cos}^{\mathrm{4}} \theta\:\mathrm{then}\:\mathrm{select}\:\mathrm{the}\: \\ $$$$\mathrm{correct}\:\mathrm{option}: \\ $$$$\left.\mathrm{i}\right)\:\mathrm{0}\:<\:\mathrm{A}\:<\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left.\mathrm{ii}\right)\:\mathrm{1}\:<\:\mathrm{A}\:<\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\left.\mathrm{iii}\right)\:\frac{\mathrm{1}}{\mathrm{2}}\:\leq\:\mathrm{A}\:\leq\:\mathrm{1} \\ $$$$\left.\mathrm{iv}\right)\:\frac{\mathrm{3}}{\mathrm{2}}\:\leq\:\mathrm{A}\:\leq\:\mathrm{2} \\ $$

Question Number 206500 Answers: 2 Comments: 0

If asin^2 θ + bcos^2 θ = c, bsin^2 φ + acos^2 φ = d and atanθ = btanφ then prove that (1/a) + (1/b) = (1/c) + (1/d) .

$$\mathrm{If}\:{a}\mathrm{sin}^{\mathrm{2}} \theta\:+\:{b}\mathrm{cos}^{\mathrm{2}} \theta\:=\:{c},\:{b}\mathrm{sin}^{\mathrm{2}} \phi\:+\:{a}\mathrm{cos}^{\mathrm{2}} \phi\:=\:{d} \\ $$$$\mathrm{and}\:{a}\mathrm{tan}\theta\:=\:{b}\mathrm{tan}\phi\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:=\:\frac{\mathrm{1}}{{c}}\:+\:\frac{\mathrm{1}}{{d}}\:. \\ $$

Question Number 206471 Answers: 1 Comments: 0

If asinθ = bcosθ = ((2ctanθ)/(1 − tan^2 θ)) then prove that (a^2 − b^2 )^2 = 4c^2 (a^2 + b^2 ).

$$\mathrm{If}\:{a}\mathrm{sin}\theta\:=\:{b}\mathrm{cos}\theta\:=\:\frac{\mathrm{2}{c}\mathrm{tan}\theta}{\mathrm{1}\:−\:\mathrm{tan}^{\mathrm{2}} \theta}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\left({a}^{\mathrm{2}} \:−\:{b}^{\mathrm{2}} \right)^{\mathrm{2}} \:=\:\mathrm{4}{c}^{\mathrm{2}} \left({a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \right). \\ $$

Question Number 206434 Answers: 1 Comments: 0

If tan^2 θ = 1 − x^2 then prove that secθ + tan^3 θcosecθ = (√((2 − x^2 )^3 )) .

$$\mathrm{If}\:\mathrm{tan}^{\mathrm{2}} \theta\:=\:\mathrm{1}\:−\:{x}^{\mathrm{2}} \:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{sec}\theta\:+\:\mathrm{tan}^{\mathrm{3}} \theta\mathrm{cosec}\theta\:=\:\sqrt{\left(\mathrm{2}\:−\:{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:. \\ $$

Question Number 206421 Answers: 1 Comments: 0

If tanpθ = ptanθ then prove that ((sin^2 pθ)/(sin^2 θ)) = (p^2 /(1 + (p^2 − 1)sin^2 θ)) .

$$\mathrm{If}\:\mathrm{tan}{p}\theta\:=\:{p}\mathrm{tan}\theta\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{sin}^{\mathrm{2}} {p}\theta}{\mathrm{sin}^{\mathrm{2}} \theta}\:=\:\frac{{p}^{\mathrm{2}} }{\mathrm{1}\:+\:\left({p}^{\mathrm{2}} \:−\:\mathrm{1}\right)\mathrm{sin}^{\mathrm{2}} \theta}\:.\: \\ $$

Question Number 206362 Answers: 2 Comments: 0

sin(π/7) × sin((2π)/7) × sin((3π)/7) = ?

$$\mathrm{sin}\frac{\pi}{\mathrm{7}}\:×\:\mathrm{sin}\frac{\mathrm{2}\pi}{\mathrm{7}}\:×\:\mathrm{sin}\frac{\mathrm{3}\pi}{\mathrm{7}}\:=\:? \\ $$

Question Number 206048 Answers: 1 Comments: 0

Prove that 2^(sin^2 θ) + 2^(cos^2 θ) ≥ 2(√2).

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{2}^{\mathrm{sin}^{\mathrm{2}} \theta} \:+\:\mathrm{2}^{\mathrm{cos}^{\mathrm{2}} \theta} \:\geqslant\:\mathrm{2}\sqrt{\mathrm{2}}. \\ $$

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Question Number 205429 Answers: 2 Comments: 0

If, ϕ = (1/2) (π −cos^( −1) ((1/4) )) ⇒ log_( 2) ( (( 1+ cos(6ϕ ))/(cos^6 (ϕ ))) ) =?

$$ \\ $$$$\:\mathrm{I}{f},\:\:\varphi\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\left(\pi\:−{cos}^{\:−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{4}}\:\right)\right) \\ $$$$ \\ $$$$\:\:\:\Rightarrow\:\mathrm{log}_{\:\mathrm{2}} \left(\:\frac{\:\mathrm{1}+\:{cos}\left(\mathrm{6}\varphi\:\right)}{{cos}^{\mathrm{6}} \left(\varphi\:\right)}\:\right)\:=? \\ $$$$ \\ $$

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Prove the following trig identity: ((2sinα+sin3α+sin5α)/(cosα−2cos2α+cos3α))=((2cos2α)/(tan(α/2)))

$$\mathrm{Prove}\:\mathrm{the}\:\mathrm{following}\:\mathrm{trig}\:\mathrm{identity}: \\ $$$$\frac{\mathrm{2sin}\alpha+\mathrm{sin3}\alpha+\mathrm{sin5}\alpha}{\mathrm{cos}\alpha−\mathrm{2cos2}\alpha+\mathrm{cos3}\alpha}=\frac{\mathrm{2cos2}\alpha}{\mathrm{tan}\frac{\alpha}{\mathrm{2}}} \\ $$

Question Number 204101 Answers: 0 Comments: 0

Find the possible values for x and y if 10cosx + 12cos(x+y)=5 10sinx + 12sin(x+y)=20.66

$${Find}\:{the}\:{possible}\:{values}\:{for}\:{x}\:{and}\:{y}\:{if} \\ $$$$\mathrm{10}{cosx}\:+\:\mathrm{12}{cos}\left({x}+{y}\right)=\mathrm{5} \\ $$$$\mathrm{10}{sinx}\:+\:\mathrm{12}{sin}\left({x}+{y}\right)=\mathrm{20}.\mathrm{66} \\ $$

Question Number 204083 Answers: 2 Comments: 0

Given that tan(A + B) = 1 and tan(A - B) = 1/7 find tan A and tan B

Question Number 204072 Answers: 1 Comments: 0

((sin^2 θ)/2)=sin 2θ? (90°>θ>0°)

$$\frac{\mathrm{sin}^{\mathrm{2}} \:\theta}{\mathrm{2}}=\mathrm{sin}\:\mathrm{2}\theta?\:\left(\mathrm{90}°>\theta>\mathrm{0}°\right) \\ $$

Question Number 203935 Answers: 2 Comments: 0

((cos(x/3)+sin (x/3))/(cos (x/3)−sin (x/3)))=?

$$\frac{{cos}\frac{{x}}{\mathrm{3}}+{sin}\:\frac{{x}}{\mathrm{3}}}{{cos}\:\frac{{x}}{\mathrm{3}}−{sin}\:\frac{{x}}{\mathrm{3}}}=? \\ $$

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