Question

Prove the above question


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Answer 1

Given :

sec θ+ tan θ = 1/(sec θ- tan θ)

To prove : LHS=RHS

Solution :

RHS =>   1/(sec θ- tan θ)

MULTIPLY  (1/(sec θ- tan θ) IN NUMERATOR ANS DENOMINATOR OF    RHS :-

=> 1/(sec θ- tan θ) * (sec θ+ tan θ)/(sec θ+ tan θ)

=> (sec θ+ tan θ)/ (sec^2 θ- tan^2 θ)

Using Identity sec^2 θ- tan^2 θ = 1

we get, RHS = sec θ+ tan θ which is equal to LHS

Hence proved that LHS=RHS

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