Question

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4. If sinA =
1 / 2, find the value of
2 sec A / 1 + tan^2 A.

Answer 1

Heya !!!




SinA = 1/2 = P/H



P = 1 and H = 2


By Pythagoras theroem,


(H)² = (P)² + (B)²


(B)² = (H)² - (P)²


(B)² = (2)² - (1)²


B² = 4-1


B = ✓3


Therefore,


SecA = B/H = ✓3/2


And,


TanA = P/B = 1/✓3



So,


2SecA / 1 + Tan²A = 2 × ✓3/2 / 1 + (1/✓3)²





=> ✓3 / 1 + 1/3



=> ✓3 / 3 + 1/3


=> ✓3/4/3



=> ✓3/4 × 1/3



=> ✓3 / 4 × 1/✓3 × ✓3



=> 1/4✓3.


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