Question

What is the answer of (1+tan+sec)(1-cos-cosec) =
want the answer with procedure​

Answer 1

Answer:

Step-by-step explanation:

(1+ cot A - cosec A)(1+tanA+secA)=2 \\ 
L.H.S. \\ 
=(1+cotA-cosecA)(1+tanA+secA) \\
= (1 + \frac{cosA}{sinA} - \frac{1}{sinA} )(1+ \frac{sinA}{cosA} + \frac{1}{cosA} ) \\
= ( \frac{sinA+cosA-1}{sinA} )( \frac{cosA+sinA+1}{cosA} ) \\
= \frac{ (sinA+cosA)^{2}- 1^{2} }{sinA.cosA} \\
= \frac{ sin^{2}A + cos^{2}A + 2sinA.cosA-1 }{sinA.cosA} \\ 
= \frac{ 1 + 2sinA.cosA-1 }{sinA.cosA} \\ 
= \frac{2sinA.cosA }{sinA.cosA} = 2 = R.H.S.

Hence, proved

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