If-P-Q-90-0-then-prove-that-sin-P-cos-Q-sin-Pcos-Q-cos-P-

Question Number 222022 by fantastic last updated on 15/Jun/25

$${If}\:\angle{P}+\angle{Q}\:=\mathrm{90}^{\mathrm{0}} \:{then}\:{prove}\:{that} \\ $$$$\sqrt{\frac{\mathrm{sin}\:{P}}{\mathrm{cos}\:{Q}}−\mathrm{sin}\:{P}\mathrm{cos}\:{Q}}=\mathrm{cos}\:{P} \\ $$

Commented by MathematicalUser2357 last updated on 17/Jun/25

You mean If ∠P+∠Q =222022^0 then prove that (√(((sin P)/(cos Q))−sin Pcos Q))=cos P

$${You}\:{mean}\:{If}\:\angle{P}+\angle{Q}\:=\mathrm{222022}^{\mathrm{0}} \:{then}\:{prove}\:{that} \\ $$$$\sqrt{\frac{\mathrm{sin}\:{P}}{\mathrm{cos}\:{Q}}−\mathrm{sin}\:{P}\mathrm{cos}\:{Q}}=\mathrm{cos}\:{P} \\ $$

Commented by fantastic last updated on 17/Jun/25

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Answered by som(math1967) last updated on 15/Jun/25

(√(((sinP)/(cos(90−P)))−sinPcos(90−P))) (√(1−sin^2 P))=cosP

$$\sqrt{\frac{{sinP}}{{cos}\left(\mathrm{90}−{P}\right)}−{sinPcos}\left(\mathrm{90}−{P}\right)} \\ $$$$\sqrt{\mathrm{1}−{sin}^{\mathrm{2}} {P}}={cosP} \\ $$

Commented by fantastic last updated on 15/Jun/25

$${thanks} \\ $$$$ \\ $$

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