Question

Sin (90-theta)÷cosec(90-theta)-cot(90-theta)

Answer 1

Answer:

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Answer 2

$\LARGE\star\mathfrak{\underline{\underline{\red{ᴀɴsᴡᴇʀ: }}}}$

$\sf{ \frac{sin(90 - \theta)}{cosec(90 - \theta) - cot(90 - \theta)} }$

$\underline{ \underline{\sf{formulae : }}} \\ \sf{sin(90 - \theta) = cos \theta} \\ \sf{ cosec(90 - \theta) = sec \theta} \\ \sf{cot (90 - \theta) = tan \theta} \\ \sf{sec \theta = \frac{1}{cos \theta} } \\ \sf{tan \theta = \frac{sin \theta}{cos \theta} } \\ \sf{sin {}^{2} \theta + cos {}^{2} \theta = 1 } \\ \sf{a {}^{2} - b {}^{2} = (a + b)(a - b)}$

$\underline{\underline{ \sf{solution : }}} \\ \sf{ \frac{sin(90 - \theta)}{cosec(90 - \theta) - cot(90 - \theta)} } \\ \\ \sf{ = \frac{cos \theta}{sec \theta - tan \theta} } \\ \\ \sf{ = \frac{cos \theta}{ \frac{1}{cos \theta} - \frac{sin \theta}{cos \theta} } } \\ \\ \sf{ = \frac{cos \theta}{ \frac{1 - sin \theta}{cos \theta} } } \\ \\ \sf{ = \frac{cos {}^{2} \theta }{1 - sin \theta} } \\ \\ \sf{ \frac{(1 - sin {}^{2} \theta)}{1 - sin \theta} } \\ \\ \sf{ = \frac{(1 - sin \theta)(1 + sin \theta)}{(1 - sin \theta)} } \\ \\ \sf{ = \frac{ \cancel{(1 - sin \theta)}(1 + sin \theta)}{ \cancel{(1 - sin \theta)}} } \\ \\ \sf{ \bold{ = \underline{ \underline{(1 + sin \theta)}}}}$