Question

Solvefi the equation : cos theta /1-sin theta + cos theta / 1+ sin theta

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Answer 1

Answer:

cos(θ)1−sin(θ)=1+sin(θ)cos(θ)

This can be proven by cross-multiplication: multiply both sides by cos(θ)(1−sin(θ)), i.e. by both denominators to get

cos2(θ)=(1+sin(θ))(1−sin(θ))

On the right hand side we have the expression (a+b)(a−b)=a2−b2, so the expression becomes

cos2(θ)=1−sin2(θ)

Which is true, because it derives immediately from the fundamental trigonometric equation

cos2(θ)+sin2(θ)=1

Step-by-step explanation:

LHS=cos(θ)1−sin(θ)

=cos2(θ)cosθ(1−sin(θ))

=1−sin2(θ)cosθ(1−sin(θ))

=(1−sin(θ))(1+sinθ)cosθ(1−sin(θ))

=1+sin(θ)cos(θ)=RHS