Question

show that costheta /1-sintheta + 1-sintheta / costheta = 2 sec theta​

Answer 1

Answer:

Use identities-

(a - b)² = a² + b² - 2ab

sin²α + cos²α = 1

Step-by-step explanation:

(cos θ) / (1 - sin θ) + (1 - sin θ) / (cos θ)

= [(cos θ)² + (1 - sin θ)²] / (cos θ)(1 - sin θ)

= [cos²θ + sin²θ + 1 - 2sin θ] / (cos θ)(1 - sin θ)

= (1 + 1 - 2sinθ) / (cos θ)(1 - sin θ)

= (2 - 2sin θ) / (cos θ)(1 - sin θ)

= 2(1 - sin θ) / (cos θ)(1 - sin θ)

= 2 / cos θ

= 2sec θ

Hence Proved.

Answer 2

Step-by-step explanation:

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