Which of the following are trigonometric identities Check al

Which of the following are trigonometric identities? Check all that apply. 4cosx sinx = 2cos x + 1 - 2sin x sec x - cos x / sec x = sin^2 x tanx cosx cscx = 1 1 - tanx tany = cos(X + Y) / cos x cos y

Solution

Options B , C , D are correct

A) 4 cosx sinx = 2cosx +1 - 2sinx is (not true)

since x = 0 ==> 4 cosx sinx = 4 cos(0) sin(0) = 0

==> 2cos(0) +1 - 2sin(0) = 2 + 1 = 3

Hence not equal

B) (secx - cosx)/secx = sin²x

consider (secx - cosx)/secx = [ (1/cosx) -cosx]/(1/cosx)

= [(1 - cos²x)/cosx]/(1/cosx)

= (1 - cos²x)

= sin²x

Hence (secx - cosx)/secx = sin²x (True)

C) tanx cosx cscx = 1

consider tanx cosx cscx = (sinx/cosx) cosx (1/sinx)

= 1

Hence tanx cosx cscx = 1 (True)

D) 1 - tanx tany = [cos(x +y)]/(cosx cosy)

consider 1 - tanx tany

= 1 - (sinx/cosx) (siny/cosy)

= 1 - (sinx siny)/(cosx cosy)

= [cosx cosy - sinx siny]/(cosx cosy)

= cos(x +y) /(cosx cosy)

Hence 1 - tanx tany = [cos(x +y)]/(cosx cosy) (True)