Question 83

If $$(secA - tanA)^2$$ = x, then the value of x is

Solution

Expression : $$(secA - tanA)^2$$

= $$(\frac{1}{cos A} - \frac{sin A}{cos A})^2$$

= $$(\frac{1 - sin A}{cos A})^2 = \frac{(1 - sin A)^2}{cos^2 A}$$

= $$\frac{(1 - sin A)^2}{1 - sin^2 A}$$

= $$\frac{(1 - sin A)^2}{(1 - sin A)(1 + sin A)}$$

= $$\frac{1 - sin A}{1 + sin A}$$

=> Ans - (C)

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