Inverse Trigonometric Functions

P → 4
(Q) cos x + cos y = - cos z
  sin x + sin y = -sin z
2 + 2 cos (x - y) = 1
⇒ cos (x - y) = -1/2
⇒ 2 cos‌2 (

x−y

2

)−1=−

1

2

⇒ cos (

x−y

2

) = 1/2Q → 3
(R) cos 2x (cos(

Π

4

−x)−cos(

Π

4

+x)) + 2 sin‌2 x = 2 sin x cos x
 cos 2x (√2sin x) + 2 sin‌2 x = 2 sin x cos x
 √2 sin x [cos 2x + √2 sin x - √2 cos x] = 0
 Either sin x = 0 OR cos‌2 x - sin‌2 x = √2 (cos x - sin x)
 sec x =1      OR cos x = sin x
        ⇒ sec x = √2
R → 2
(S) cot( sin−1√1−x2) = sin (tan −1(x√6))
 

x

√1−x2

= x

√6

√1+6x2

  ⇒ 1 + 6x‌2 = 6 - 6x‌2
  ⇒ 12x‌2 = 5
 x = √

5

12

=

1

2

√

5

3