SinA/1-cosA=cosecA+cotA
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Step-by-step explanation:
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HEY MATE HERE IS THE ANSWER
Step-by-step explanation:
To prove : \frac{\sin A}{1+\cos A}=\csc A-\cot A
1+cosA
sinA
=cscA−cotA
Proof :
Taking LHS,
\frac{\sin A}{1+\cos A}
1+cosA
sinA
Rationalize,
=\frac{\sin A}{1+\cos A}\times \frac{1-\cos A}{1-\cos A}=
1+cosA
sinA
×
1−cosA
1−cosA
=\frac{\sin A(1-\cos A)}{(1+\cos A)(1-\cos A)}=
(1+cosA)(1−cosA)
sinA(1−cosA)
=\frac{\sin A(1-\cos A)}{1^2-\cos^2 A}=
1
2
−cos
2
A
sinA(1−cosA)
=\frac{\sin A(1-\cos A)}{\sin^2 A}=
sin
2
A
sinA(1−cosA)
=\frac{1-\cos A}{\sin A}=
sinA
1−cosA
=\frac{1}{\sin A}-\frac{\cos A}{\sin A}=
sinA
1
−
sinA
cosA
=\csc A-\tan A=cscA−tanA
= RHS
So, LHS=RHS hence proved.
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