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prove that √1+sin θ/1-sin θ+√1-sin θ/1 + sin θ =2sec θ

prove that √1+sin θ/1-sin θ+√1-sin θ/1 + sin θ =2sec θ

Grade:10

2 Answers

Arun
25750 Points
6 years ago
On taking LCM
1 + sin\theta + 1 - sin\theta/(\sqrt(1-sin\theta)(1+ sin\theta)
= 2/\sqrt(1 - sin²\theta)
= 2/ cos \theta
= 2 sec\theta
 
Hence proved
Happy learning
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the solution to your problem.
 
On taking LCM
[(1 + sinθ) + (1 – sinθ)] / [√(1 – sinθ)(1 + sinθ)]
= 2/√(1 – sin²θ)
= 2/cosθ
= 2secθ
Hence proved
 
Thanks and regards,
Kushagra

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