Prove that : 1-sinA/1+sinA=(secA-tanA)2

Asked by giridipak451 | 4th Oct, 2019, 10:01: PM

Expert Answer:

To prove:- 1-sinA/1+sinA=(secA-tanA)2
L H S equals fraction numerator 1 minus sin A over denominator 1 plus sin A end fraction
equals fraction numerator 1 minus sin A over denominator 1 plus sin A end fraction cross times fraction numerator 1 minus sin A over denominator 1 minus sin A end fraction
equals fraction numerator open parentheses 1 minus sin A close parentheses squared over denominator 1 minus sin squared A end fraction equals fraction numerator open parentheses 1 minus sin A close parentheses squared over denominator cos squared A end fraction
equals open parentheses fraction numerator 1 minus sin A over denominator cos A end fraction close parentheses squared
equals open parentheses fraction numerator 1 over denominator cos A end fraction minus fraction numerator sin A over denominator cos A end fraction close parentheses squared
equals open parentheses s e c A minus tan A close parentheses squared
equals R H S
H e n c e comma space p r o v e d.

Answered by Renu Varma | 7th Oct, 2019, 10:18: AM