Question

if tanA=2,prove that sinAsecA+tanA-cosecA=8-√5/2​

Answer 1

Answer:

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Answer 2

Answer:

$\tan(a) = 2 \\ \tan(a) = \frac{p}{b} \\ \frac{p}{b} = 2 \\ p = 2 \: \: and \: b = 1 \\ h = \sqrt{p {}^{2} + b {}^{2} } \\ h = \sqrt{2 {}^{2} + 1 {}^{2} } \\ h = \sqrt{4 + 1} \\ h = \sqrt{5} \\ now \\ \sin(a) \sec(a) + \tan(a) - cosec(a) \\ = \frac{2}{ \sqrt{5} } \times \frac{ \sqrt{5} }{1} + 2 - \frac{ \sqrt{5} }{2} \\ = 2 + 2 - \frac{ \sqrt{5} }{2} \\ = \frac{4 + 4 - 5}{2} \\ = \frac{8 - \sqrt{5} }{2} ans.$