Question

If cosecA + cotA= m
show that m²-1/m²+1 = cosA​

Answer 1

Answer:

answer is as follow.....

Step-by-step explanation:

Given: cosec A + cot A = m

⇒ (cosec A + cot A)2 = (m)2 [squaring both sides ]

⇒ cosec2A + cot2A + 2 cosec A cot A = m2 .......(1)

Now, LHS

=m2−1m2+1

= cosec2A+cot2A+2 cosecAcotA−1 cosec2A+cot2A+2 cosceA⋅cotA+1. [ From (1) ]

=cot2A+cot2A+2 cosecA⋅cotA cosec2A+ cosec2A+2 cosecA⋅cotA [Since, Cosec2A - Cot2A = 1]

=2cot2A+2 cosecAcotA2 cosec2A+2 cosecAcotA

=2cotA(cotA+ cosecA)2 cosecA( cosecA+cotA)

=cotAcosecA

=cosAsinA1sinA

=cosAsinA×sinA1

= cos A = RHS

Hence, Proved.

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Answer 2

Step-by-step explanation:

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