Question

Sec^2A×cosec^2A=tan^2A+cos^2A+2

Answer 1

${sec}^{2} a \: \times \: {cosec}^{2} a \\ = (1 + {tan}^{2} a)(1 + {cot}^{2} a) \\ = 1 + {cot}^{2} a + {tan}^{2} a + {tan}^{2} a \: {cot}^{2} a \\ = 1 + {cot}^{2} a + {tan}^{2} a + {tan}^{2} a( { \frac{1}{{tan}^{2}a } }^{2}) \\ = 1 + {cot}^{2} a + {tan}^{2} a + 1 \\ = 2 + {cot}^{2} a + {tan}^{2} a$

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