Question

tan theta/sec theta-1 + tan theta/sec theta+1 is equal to (a) 2tantheta (b) 2sectheta (c) 2cosectheta (d) 2tanthetasectheta​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Identity used:

• sec²Ф - 1 = tan²Ф

Given:

$\implies \dfrac{tan\:\theta}{sec\:\theta-1} + \dfrac{tan\:\theta}{sec\:\theta+1}\\\\\\\text{Taking Tan }\theta \text{ commonly outside, we get:}\\\\\\\implies tan\:\theta \times \left[\dfrac{1}{sec\:\theta-1}+\dfrac{1}{sec\:\theta+1}\right] \\\\\\\implies tan\:\theta \times \left[\dfrac{sec\:\theta+1+sec\:\theta-1 }{sec^2\:\theta-1}\right]\\\\\\\implies tan\:\theta \times \left[\dfrac{2sec\:\theta }{tan^2\:\theta}\right]\\\\\\\implies \dfrac{2sec\:\theta}{tan\:\theta} = \boxed{2\:cosec\:\theta}$

Hence Option (C) is the right answer.