Sec2 27° – Cot2 63° =A) 3 B) 0 C) 1 D) 2

1.	Sec2 27° – Cot2 63° =A) 3 B) 0 C) 1 D) 2
Answer» Correct option is: C) 1 \(sec^2 \,27^\circ – cot^2 \,63^\circ\) = \(1 + tan^2 \, 27^\circ - cot^2\, 63^\circ \) (\(\because\) \(sec^2 \theta = 1 + tan^2\theta\)) = \(1 + tan^2 (90^\circ - 63^\circ) - cot^2\, 63^\circ\) ( \(\because\) \(27^\circ\) = \(90^\circ\) - \(63^\circ\)) = \(1 + cot^2 \, 63^\circ - cot^2\, 63^\circ\) (\(\because\) tan (\(90^\circ\) -\(\theta\)) = cot \(\theta\)) = 1 Correct option is: C) 1

Answer»

Correct option is: C) 1

\(sec^2 \,27^\circ – cot^2 \,63^\circ\)

= \(1 + tan^2 \, 27^\circ - cot^2\, 63^\circ \) (\(\because\) \(sec^2 \theta = 1 + tan^2\theta\))

= \(1 + tan^2 (90^\circ - 63^\circ) - cot^2\, 63^\circ\) ( \(\because\) \(27^\circ\) = \(90^\circ\) - \(63^\circ\))

= \(1 + cot^2 \, 63^\circ - cot^2\, 63^\circ\) (\(\because\) tan (\(90^\circ\) -\(\theta\)) = cot \(\theta\))

= 1

Correct option is: C) 1

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