Question

Express Cos A, tan A, sec A in terms of sin A.​

Answer 1

Answer:

cosA= 1−sin 2 A →(1)as, cos 2 θ+sin 2 θ=1

tanA= cosAsinA

= 1−sin 2 AsinA ( from (1) ) & secA= cosA1

= 1−sin A1 ( From (1) )so, cosA= 1−sin 2 A

,tanA= 1−sin 2 AsinA

&

secA= 1−sin 2 A1

Answer 2

Since,cos²A+sin²A=1

cos²A=1-sin²A

cosA=+-

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

Here A is acute

& cosA is positive when A is acute

so, cosA=

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

secA

secA =

$\frac{1}{cos \: a}$

secA=

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