Prove that : √2+tan2 θ+cot2 θ=tan θ+cot θ

Asked by harshrajesh9 | 28th Jul, 2020, 12:52: PM

Expert Answer:

To prove: √(2+tan2θ+cot2θ) = tan θ+cot θ
square root of 2 plus tan squared straight theta plus cot squared straight theta end root
equals square root of 2 cross times 1 over tanθ cross times tanθ plus tan squared straight theta plus cot squared straight theta end root
equals square root of 2 cross times cotθ cross times tanθ plus tan squared straight theta plus cot squared straight theta end root
equals square root of open parentheses tanθ plus cotθ close parentheses squared end root
equals tanθ plus cotθ
Hence comma space square root of 2 plus tan squared straight theta plus cot squared straight theta end root equals tanθ plus cotθ

Answered by Renu Varma | 28th Jul, 2020, 07:40: PM