Question

Prove that (sin4a - cos4a + 1)cosec2a = 2

Answer 1

Solution of your question is here⏬⏬

(sin4a -cos4a+1)cosec2a

=[{(sin2a)+(cos2a)2}+1]cosec2a

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

=(sin2a-cos2a+1)cosec2a

[°°sin2a+cos2a=1]

={sin2a +(1-cos2a)}cosec2a

=(sin2a+sin2a)cosec2a

=2sin2a.cosec2a

=2sin2a×1/sin2a

=2

L.H.S.=R.H.S.

Hence,proved!!✅✅

Answer 2

[ Sin^4-cos^4+1 ] cosec^2 =2

LHS:

=>[(Sin^2+ cos^2)(sin^2-cos^2)+1]cosec^2

=>[Sin^2-cos^2 +1] cosec^

{as, sin^2+cos^2=1}

=Sin^2*cosec^2-cos^2*cosec^2+cosec^2

=>1-cosec^2(cos^-1)

=>1-cosec^2(-sin^2)

=>1-(-1) {as, cosec^2=1/sin^2}

=>1+1

=>2,,

RHS:

=>2

HENCE, LHS=RHS.