Question

Express the ratios cos A, tan A and sec A in the terms of sin A.​

Answer 1

Question:

Express the ratios cos A, tan A and sec A in the terms of sin A.

Answer:

cos²A+sin²A=1

Therefore,

cos²A = 1-sin²A, i.e., cosA = $\frac{ + }{} \sqrt{1 - sin {}^{2} \: a }$

This gives

cosA = $\sqrt{1 - sin {}^{2} a}$

Hence,

tanA = $\frac{sin \: a}{cos \: a} = \frac{sin \: a}{ \sqrt{1 - sin {}^{2} } \: a}$

, sec A = $\frac{1}{cos \: a} = \frac{1}{ \sqrt{1 - sin {}^{2} } a}$