Question

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Answer 1

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\sqrt{1+cosA/1-cosA}

\sqrt{(1+cosA/1-cosA)*(1+cosA/1+cosA)}

\sqrt{(1+cosA)^2/(1-cos^2A)}

(1+cosA)/sinA;             [\sqrt{1-cos^2A}=sinA]

(1/sinA)+(cosA/sinA);

cosecA+cotA

proved.......

yes!

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Answer 2

hey
your question answer is.
we have to prove LHS equal to RHS.
so first we take RHS.
that is.

cosec A+cot A

1/sin A+cos A/sin A

1+cos A/sin A .....1eq

now taking LHS.
that is.

✓1+cos A/✓1-cos A

rationalise it
we get

✓1+cos A/✓1-cos A×✓1+cos A/✓1+cos A

✓1+cos A×✓1+cos A/✓1-cos A×✓1+cos A

✓(1+cos A)^2
__________. we know
✓(1-cos A)(1+cos A). (a+b)(a-b)=a^2-b^2...8eq


1+cos A. as root cancel from square
__________
✓1^2-cos A^2.by 8eq 1 ^2-cosA^2=sinA^2
.......6eq

1+cos A
______
✓sin^2A. by ..6eq


1+cos A
_____
sin A. as root cancelled from square


1+cos A
______.......2eq
sin A

hence
1eq=2eq
LHS=RHS

hence proved
___________


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