Question

(cos^2A-1)(cot^2A+1)=-1​

Answer 1

Answer:

cos 2A + 1/( cosec2A)

( 1+ cot2A=cosec2A)

cos 2A+1/1/SIN2 A (COSEC2A=1/SIN2A)

COS2A + SIN2A=1

Answer 2

Step-by-step explanation:

To prove : $(\cos^2A-1)(\cot^2A+1)=-1$

Proof :

Taking LHS,

$LHS=(\cos^2A-1)(\cot^2A+1)$

Using identity of trigonometry,

$\sin^2A+\cos^2 A=1 \Rightarrow \cos^2 A-1=-\sin^2A$

and $\cot^2 A+1=\csc^2A$

Substitute above,

$LHS=(-\sin^2A-1)(\csc^2A)$

$LHS=(-\sin^2A-1)(\frac{1}{\sin^2 A})$

$LHS=-1$

LHS=RHS hence proved.

#Learn more

Prove that 1/(1+cot^2A)+cos*2A=1

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