sec²a.cosec²a = tan²a + cot²a+ 2

Asked by rakshitsujata1 | 7th Apr, 2021, 08:44: AM

Expert Answer:

To prove: sec²a.cosec²a = tan²a + cot²a+ 2
Consider the RHS
= tan²a + cot²a+ 2
= (sin2a/cos2a) + (cos2a/sin2a) + 2
= (sin4a+cos4a+2cos2a sin2a)/(cos2a sin2a)
= (sin2a+cos2a)2/(cos2a sin2a)
= 1/(cos2a sin2a)
= sec2a cosec2a

Answered by Renu Varma | 9th Apr, 2021, 10:44: AM