Let f(x) = loge(sin x), (0 < x < $\pi $) and g(x) = sin–1 (e–x ), (x $ \ge $ 0). If $\alpha $ is a positive real number such that a = (fog)'($\alpha $) and b = (fog)($\alpha $), then :

Question

Let f(x) = log_e(sin x), (0 < x < $\pi $) and g(x) = sin^–1 (e^–x ), (x $ \ge $ 0). If $\alpha $ is a positive real number such that a = (fog)'($\alpha $) and b = (fog)($\alpha $), then :

a$\alpha $² + b$\alpha $ - a = -2$\alpha $²

a$\alpha $² + b$\alpha $ + a = 0

a$\alpha $² - b$\alpha $ - a = 0

a$\alpha $² - b$\alpha $ - a = 1

Solution

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