Question

Sin2(90-theta)+cos2(90-theta) is equal to

Answer 1

a) Find sinθtanθ, given cosθ=2/3 b) Simplify sin(180∘ −θ)+cosθ⋅tan(180∘ + θ). c) Solve cos^2 x−

Step-by-step explanation:

Let's simplify the expression step by step:

1. Start with the trigonometric identities for sine and cosine of complementary angles:

- s in(90 - θ) = cos(θ)

- cos(90 - θ) = sin(θ)

2. Substitute these identities into the expression:

- sin^2(90 - θ) + cos^2(90 - θ) = [cos(θ)]^2 + [sin(θ)]^2

3. Now, remember the Pythagorean trigonometric identity:

- sin^2(θ) + cos^2(θ) = 1

4. Apply the Pythagorean identity to the expression:

- [cos(θ)]^2 + [sin(θ)]^2 = 1

So, sin^2(90 - θ) + cos^2(90 - θ) is equal to 1.