Question

Express : sin , tan , A A cotA and cosecA in terms of sec A.
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Answer 1

Answer:

sinA = $\frac{\sqrt{sec^{2}A-1}}{secA}$

tanA = $\sqrt{sec^{2}A-1}$

cotA = $\frac{1}{\sqrt{sec^{2}A-1}}$

cosecA = $\frac{secA}{\sqrt{sec^{2}A-1}}$

Step-by-step explanation:

(i) w.k.t., secA = 1/cosA and sin²A = 1-cos²A

⇒ sin²A = 1 - 1/sec²A = sec²A-1 / sec²A

⇒ sinA = $\frac{\sqrt{sec^{2}A-1}}{secA}$

(ii) w.k.t., tan²A = sec²A - 1

⇒ tanA = $\sqrt{sec^{2}A-1}$

(iii) w.k.t., cotA = 1/tanA and tanA = $\sqrt{sec^{2}A-1}$

⇒ cotA = $\frac{1}{\sqrt{sec^{2}A-1}}$

(iv) w.k.t., cosecA = 1/sinA and sinA = $\frac{\sqrt{sec^{2}A-1}}{secA}$

⇒ cosecA = $\frac{secA}{\sqrt{sec^{2}A-1}}$

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