Given that angle A is not an integer multiple of pi2 A noteq

Given that angle A is not an integer multiple of pi/2 (A notequalto) which of the following are true? sec^2 x - tan^2 x = 1 cot^2 x - csc^2 x = -1 sin^2 x - csc^2 x + cos^2 x + sec^2 x - tan^2 x + cot^2 x = 1 cos x. sec x = 1 2 cos^2 x - cos(2x) = 1 sin^2 x + cos^2 x = 1 tan x. cot x + cos x sec x - sin x. csc x = 1 cos(2x) + 2 sin^2 (x) = 1

Solution

AS per trigonometric identity:

1+tan^2x +sec^2x

sec^2x -tan^2x = 1

So, True

2) Trig identity : 1+cot^2x = csc^2x

So, cot^2x -csc^2x =1

True

3) sin^2x -csc^2x +cos^2x +sec^2x -tan^2x +cot^2x =1

LHS = sin^2x +cos^2x + (sec^2x -tan^2x) +( (cot^2x -csc^2x)

= 1 -(1) +1

= 1

True

4) cosx *secx = cosx/cosx =1

True

5) 2cos^2x -cos2x =1

cos2x = 2cos^2x -1

So, 2cos^2x -cos2x =1

So, True

6) sin^x +cos^x =1

True

7) tanx*cotx +cosx*secx -sinxcscx =1

LHS tanx/tanx +cosx/cosx -sinx/sinx

= 1+1-1

=1

8) cos2x = 1-2sin^2x =1

So, cos2x +2sin^2x =1

So, True