Chapter 6 – Trigonometry – Text Book Solution
Problem set 6| Q 5.6| Page 138
Prove the following. 1 1 − sin θ + 1 1 + sin θ = 2 sec 2 θ
[frac{1}{1 – sintheta} + frac{1}{1 + sintheta}]
[ = frac{1 + sintheta + 1 – sintheta}{left( 1 – sintheta right)left( 1 + sintheta right)}]
[ = frac{2}{1 – sin^2 theta} left[ left( a – b right)left( a + b right) = a^2 – b^2 right]]
[ = frac{2}{cos^2 theta} left( sin^2 theta + cos^2 theta = 1 right)]
[ = 2 sec^2 theta]
Solution
[1/(1 – sin theta) + 1/(1 + sin theta)] = (1 + sin theta + 1 – sin theta) / ((1 – sin theta)(1 + sin theta)) = 2 / (1 – sin^2 theta) [ (a – b)(a + b) = a^2 – b^2 ] = 2 / cos^2 theta [sin^2 theta + cos^2 theta = 1] = 2 sec^2 theta
Chapter 6 – Trigonometry – Text Book Solution
Problem Set 6 |Q 5.6| P 138
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