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sqrt((A*cosec %2B 1)/(A*cosec - 1))=tan(A) %2B sec(A) |
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Answer» LHS : (secA + tanA)² ( 1/cosA + sinA/cosA)² (1 + sinA)² / cos²A we know that , cos²A =1 - sin²A (1+sinA) (1 + sinA) / {1 - sin²A} Also , 1 - sin²A =(1+sinA) (1 - sinA) [∵a² -b² = (a+b) (a - b) ] (1+sinA) (1 + sinA) /(1+sinA) (1 - sinA) (1 + sinA )gets cancelled on numerator and denominator , => 1 + sinA / 1 - sinA sinA = 1/cosecA => 1 + ( 1/cosecA) / [ 1 - (1/cosecA) ] =>cosecA+1/cosecA÷cosecA-1/cosecA => cosec A gets cancelled ,on both sides , hence , LHS becomes , cosecA + 1/cosecA - 1 |
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