Question

sec theta - tan theta sin theta simply the following expression​

Answer 1

Answer:

Tan x/(cos x - sec x)=

Tan x/(cos x- 1/cos x)

=Tan x/( cos^2 x - 1)/cos x. Taking lcm

=Tan x/-sin^2 x/cos x. Using trig identity

=Tan x*cos x/- sin^2 x

=Sin x/-sin^2 x

=-sin x/sin^2 x

=-1/sin x

= - cosec x

(OR)

Tan x/(cos x - sec x)

=√Tan ^2 x/(1/sec x ) - sec x )

=√(sec^2 x- 1)/( 1- sec^2 x)/sec x taking lcm in the denominator

=- √(sec^2 x - 1)*sec x/(sec^2 x -1)

=-sec x/√(sec^2 x - 1)

=-sec x/tan x

=-sec x * cot x

=-1/cos x * cos x/sin x

=-1/sin x

=- cosec x