If sin (theta) = (frac{m – n}{m + n}); Find the value of 1 + tan2(theta)
-
A.
(frac{(m^2 + n^2)}{m + n}) -
B.
(frac{(m^2 + n^2 + 2mn)}{4mn}) -
C.
(frac{2(m^2 + n^2 + mn)}{m + n}) -
D.
(frac{(m^2 + n^2 + mn)}{m + n})
Correct Answer: Option B
Explanation
((m + n)^{2} = (m – n)^{2} + x^{2})
(m^{2} + 2mn + n^{2} = m^{2} – 2mn + n^{2} + x^{2})
(x^{2} = 4mn)
(x = sqrt{4mn} = 2sqrt{mn})
1 + tan2(theta) = sec2(theta)
= (frac{1}{cos^2theta})
(cos theta = frac{2sqrt{mn}}{(m + n)})
(frac{1}{cos theta} = frac{(m + n)}{2sqrt{mn}})
(sec^{2} theta = frac{(m + n)^{2}}{4mn})
= (frac{(m^2 + n^2 + 2mn)}{4mn})