Question

Please help me trigonometry sums

Answer 1

Hope u like my process
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Note:
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$= > \bf \: \sin ^{2} (x) + \cos ^{2} (x) = 1$
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$= > \bf \: \frac{ \sin( \theta ) }{1 - \cos( \theta ) } \\ \\ = \frac{ \sin( \theta)(1 + \cos( \theta ) ) }{(1 - \cos( \theta ) )(1 + \cos( \theta )) } \\ \\ = \frac{ \sin( \theta ) + \sin( \theta ) \cos( \theta ) }{1 - \cos ^{2} ( \theta ) } = \frac{ \sin( \theta ) + \sin( \theta ) \cos( \theta ) }{ \sin ^{2} ( \theta ) } \\ \\ = \frac{ \sin( \theta ) }{ \sin ^{2} ( \theta ) } + \frac{ \sin( \theta ) \cos( \theta ) }{ \sin ^{2} ( \theta ) } \\ \\ \bf \: = \cosec( \theta ) + \cot( \theta ) ...... < proved >$
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Hope this is ur required answer

Proud to help you

Answer 2

sin●/1-cos●
multiply the equation with1+cos●
sin●(1+cos●)/1^2-cos^2●
sin●(1+cos●)/sin^2●
1+cos●/sin write the equation as two terms
then
1/sin●+cos/sin
=cosec●+cot●
I hope it is helpful