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Question

Prove that

1(sec θtan θ)1cos θ=1cos θ1(sec θ+tan θ) [4 MARKS]

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Solution

Concept: 2 Marks
Application: 2 Marks

We have

LHS
1sec θtan θ1cos θ

=1(sec θtan θ)×(sec θ+tan θ)(sec θ+tan θ)sec θ

=(sec θ+tan θ)(sec2 θtan2 θ)sec θ

=(sec θ+tan θ)sec θ [sec2 θtan2 θ=1]

=tan θ


RHS
1cos θ1(sec θ+tan θ)

=sec θ1(sec θ+tan θ)×(sec θtan θ)(sec θtan θ)

=sec θ(sec θtan θ)(sec2 θtan2 θ)

=sec θ(sec θtan θ) [sec2 θtan2 θ=1]

=tan θ

LHS = RHS

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