Question

find the values of sin 2a, cos2a and tan 2a, when:
(ii) cos a =3/5,

Answer 1

Answer:

Given: Cos a =3/5

To find: Sin2a , cos 2a , tan 2a

Solution:

Cos a =3/5............(Given)

Now,

Cos 2a = 1- 2cos²a = 1-2(3/5)² 1- 2(9/25) = 1- 18/25

= 25-18/25= 7/25

Now,

Cos²a + sin²a = 1

(3/5)² + sin²a = 1

9/25 + sin²a = 1

sin²a = 1- 9/25

sin²a = 25-9/25

sin²a = 16/25

Sin a = 4/5 ..........( Taking +ve square roots from both

sides)

Hence,

Sin2a = 2 sin a cos a

= 2(4/5) (3/5)

= (8/5)(3/5)

= 24/25

Now,

tan 2a = Sin2a / cos 2a = 24/25/7/25= 24/7

Therefore,

Therefore, The value of Sin2a, cos2a and tan 2a is 24/25,7/25 and

24/7