Question

How will be prove that sinA(1+tanA) +cosA(1 +cotA) =secA +cosecA

Answer 1

​sinA[1+tanA]+cosA[1+cotA]​​
=sinA+sinAtanA+cosA+cosAcotA​​
=sinA+sinA×​cosA​​sinA​​+cosA+cosA×​sinA​​cosA​​​​=sinA+​cosA​​sin​2​​A​​+cosA+​sinA​​cos​2​​A
​​​​=sinA+​sinA​​cos​2​​A​​+cosA+​cosA​​sin​2​​A
​​​​=​sinA​​sin​2​​A+cos​2​​A​​+​cosA​​cos​2​​A+sin​2​​A
​​​​=​sinA​​1​​+​cosA​​1​​​​
=secA+cosecA


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