Question

(sin^4a-cos^4a+1)cosec^2a=2

Answer 1

(sin⁴a - cos⁴a + 1)cosec²a

= {(sin²a)²- (cos²a)²} + 1 }cosec²a

= {(sin²a + cos²a)(sin²a-cos²a) + 1}cosec²a

= (sin²a - cos²a + 1)cosec²a [sin²θ+cos²θ = 1]

= {sin²a + (1-cos²a)}cosec²a

= (sin²a + sin²a)cosec²a

= 2sin²a × cosec²a

= $\bf{2sin^{2}a\dfrac{1}{sin^{2}a}}$

= 2

Answer 2

Answer:

Refer the attached picture.