How to simplify Cos theta/(1 + sin theta) + tan theta?

Rowan Stuart

Rowan Stuart

Answered question

2023-01-21

How to simplify cosθ1+sinθ+tanθ?

Answer & Explanation

Giaj5sf

Giaj5sf

Beginner2023-01-22Added 8 answers

=cosθ1+sinθ+tanθ
=cosθ1+sinθ+sinθcosθ
->Get a common denominator
=cosθ1+sinθcosθcosθ+sinθcosθ1+sinθ1+sinθ
=cos2θ+sinθ+sin2θcosθ(1+sinθ)
->cos2θ+sin2θ=1
=sinθ+1cosθ(1+sinθ)
-> In the numerator and denominator, cancel out
=1cosθ
=secθ

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