Costheta - sintheta + 1/ costheta+sintheta -1= cosec theta/cos theta
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Answer:
Proved
Step-by-step explanation:
cosθ - sinθ - 1 / cosθ + sinθ - 1
dividing both numerator and denominator by sinθ
cotθ - 1 + cosecθ / cotθ + 1 -cosecθ
= cotθ - (cosec²θ - cot²θ) + cosecθ / cotθ + 1 - cosecθ
= cotθ + cosecθ - (cosecθ - cotθ)(cosecθ + cotθ) / cotθ - cosecθ + 1)
= (cosecθ + cotθ)( 1 - cosecθ + cotθ) / (1 - cosecθ + cotθ) = cosecθ + cotθ
hence proved
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