Question

prove that :secA-tanA/cosecA+cotA = cosecA-cotA/secA+tanA​

Answer 1

Step-by-step explanation:

LHS

= (SecA - TanA)/(CosecA - CotA)

Multiply and divide by SecA + TanA

= (SecA + TanA)(SecA - tanA)/(SecA + TanA)(CosecA - CotA)

= (Sec²A - Tan²A)/(SecA + TanA)(CosecA - CotA)

Sec²A - Tan²A = 1

= 1/(SecA + TanA)(CosecA - CotA)

Multiply and divide by CosecA + CotA

= (CosecA + CotA)/(SecA + TanA)(CosecA - CotA)  (CosecA + CotA)

=  (CosecA + CotA)/(SecA + TanA)(Cosec²A - Cot²A)

Cosec²A - Cot²A = 1

= (CosecA + CotA)/(SecA + TanA).1

= (CosecA + CotA)/(SecA + TanA)

= RHS

Hence Proved

Answer 2

Step-by-step explanation:

Please refer to the images attached.

I have used the rule of both side complicated (this rule is mentioned in the first image last line)

Hope it helps you. :)