Question

tan^2 theta by (sec theta - 1)^2 = 1 + cos theta by 1 - cos theta​

Answer 1

Answer:

Step-by-step explanation:

Tan²θ / (sec θ-1)²=(1+cosθ)/(1-cosθ)

Tan² θ= sec² θ-1 = (sec θ - 1)(sec θ +1)

(sec θ - 1)(sec θ +1)/(sec θ-1)²=(1+cosθ)/(1-cosθ)

(1+sec θ)/(secθ-1) = (cosθ+1)/(1-cosθ)

(1 + sec θ)(1-cos θ)=(cos θ+1)(sec θ-1)

1 - cos θ + sec θ - sec θ*cos θ = cos θ*sec θ - cos θ +sec θ - 1

Cos θ × sec θ = 1

1 - cos θ + sec θ-1 = 1- cos θ + sec θ - 1

- cos θ + sec θ = - cos θ + sec θ

0 = 0

∴ proved

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Answer 2

Tan^2 theta by ( sec theta - 1 )^2 = 1+ cos theta by 1 - cos theta