If sin A = 5/13, find the value of sin^4 A + cos^4 A.
21361/28561
Given \(\sin A = \frac{5}{13}\), using the Pythagorean identity, \(\cos A = \sqrt{1-\sin^2 A} = \sqrt{1-\frac{25}{169}} = \frac{12}{13}\).
Using the identity \(\sin^4 A + \cos^4 A = (\sin^2 A + \cos^2 A)^2 - 2\sin^2 A\cos^2 A = 1 - 2\sin^2 A\cos^2 A\).
Here \(\sin^2 A = \frac{25}{169}\) and \(\cos^2 A = \frac{144}{169}\), so \(\sin^2 A \cos^2 A = \frac{25 \times 144}{169^2} = \frac{3600}{28561}\).
So \(1 - 2\times\frac{3600}{28561} = \frac{28561 - 7200}{28561} = \frac{21361}{28561}\).
Hence, the answer is 21361/28561.
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If cosec θ = 13/12, then sin θ + cos θ - tan θ is equal to:
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