Question

question verify the trigonometric identity where 1 + sin theta divided by cos theta + cos theta divided by 1 + sin theta minus two secant theta​

Answer 1

Explanation:

cos(θ)1+sin(θ)+1+sin(θ)cos(θ)

Multiply the left fraction by cos(θ) and the right fraction by (1+sin(θ)) to put everything under the same denominator:

=(cos(θ))2+(1+sin(θ))2(1+sin(θ))⋅cos(θ)

Then we open the parentheses (at the numerator, just leave the denominator untouched) and get:

=cos2(θ)+1+2sin(θ)+sin2(θ)(1+sin(θ))⋅cos(θ)

You should remember the identity cos2(θ)+sin2(θ)=1which you can see in the numerator. So we get:

=1+2sin(θ)+1(1+sin(θ))⋅cos(θ)

which simplifies to:

=2+2sin(θ)(1+sin