Question

simplify sin theta cos 90 minus theta + 1 by 1 + tan square theta

Answer 1

(sin theta ×sin theta +1)/1+tan2theta
sin2theta+1/1+tan2theta
sin2theta+1/sec2theta
tan2theata + cos square theta

Answer 2

Answer:

1

Step-by-step explanation:

Hi,

Given expression is

sin(θ)*cos(90 - θ) + 1/(1 + tan²θ)

But we know that 1 + tan²θ = sec²θ,

Hence, given expression would become

sin(θ)*cos(90 - θ) + 1/sec²θ

Also, We know 1/secθ = cosθ,

hence 1/sec²θ = cos²θ,

hence given expression will be

sin(θ)*cos(90 - θ) + cos²θ

cos(90 - θ) = sin θ,

So, we can write given expression as

sin θ*sin θ + cos²θ

= sin²θ + cos²θ

= 1.

Hope, it helps !