cos A cot A
1 - sin A
= 1 + cosec A.
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▪We can proof this identity by taking LHS and RHS separately.....
☆LHS :
-= 1/cosec A- cot A -1/sin A
= cosec2 A - cot2A / cosec A - cot A - cosecA (since cosec2 A - cot2A = 1 and 1/sin A = cosec A)
= (cosec A - cot A) (cosec A + cot A) /(cosec A - cot A) - cosec A (since a2- b2= (a - b)(a+ b) )
= cosec A+ cot A -cosec A
= cot A
▪ In the similar way, solve RHS. In the place of 1/ sinA = cosec A and write1 = cosec2A - cot2Ain the second term.
▪You will get cot A. Since LHS and RHS give out cot Aas answer, this prooves the identity...
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