Question
Download Solution PDFThe value of (cosec A + cot A)(1 - cos A) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
(cosec A + cot A)(1 - cos A)
Formula Used:
cos2A + sin2A = 1
cosec A = \(\frac{1}{sin\ A}\)
cot A = \(\frac{cos\ A }{ sin\ A}\)
Calculation:
⇒ (cosec A + cot A)(1-cos A) = \((\frac{1}{sin A} + \frac{cos A}{sinA})(1-cos A) =\frac{1+cosA}{sinA}(1-cosA)=\frac{1-cos^2A}{sinA}=\frac{sin^2A}{sinA}\) = sin A
⇒ Hence, The value of (cosec A + cot A)(1 - cos A) is sin A
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