Question

if cos9a=sina&9a<90dergee then find the tan5a value

Answer 1

Answer:

cos9a=sina

cosa=cos(90-a)

9a=90-a

9a+a=90

10a=90⁰

a=9⁰

tan5a=?

tan5×9⁰=tan45⁰

we know that, tan45⁰=1

Hence, tan5a=1

Answer 2

Given :

cos9a = sina

To Find :

The value of tan5a

Solution :

∴ cos9a = sina

or,  cos9a = cos (90-a) {as sina = cos(90 - a)}

or,        9a = 90 - a

or,       10a = 90

or,           a = $\frac{90}{10}$

∴             a = 9

∴ tan5a

= tan(5×9)   (∵ a = 9)

= tan45°

= 1

∴ The value of Tan5a is 1 when a = 9.