Question

please answer this question.....

Answer 1

Tn=sin^n@+cos^2n@
T1=sin@+cos@
T3=sin^3@+cos^3@
T5=sin^5@+cos^5@
T7=sin^7@+cos^7@

LHS=(T3-T5)/T1=(sin^3@+cos^3@-sin^5@-cos^5@)/(sin@+cos@)

={sin^3 @(1-sin^2@)+cos^3@(1-cos^2@)}/(sin@+cos@)

=(sin^[email protected]^2@+cos^[email protected]^2@)/(sin@+cos@)

=sin^[email protected]^2@(sin@+cos@)/(sin@+cos@)

=sin^[email protected]^2@

now
RHS=(T5-T7)/T3

=(sin^5@+cos^5@-sin^7@-cos^7@)/(sin^3@+cos^3@)

={sin^5@(1-sin^2@)+cos^5@(1-cos^2@)}/(sin^3@+cos^3@)

=(sin^[email protected]^2@+cos^[email protected]^2@)/(sin^3@+cos^3@)

=sin^[email protected]^2@(sin^3@+cos^3@)/(sin^3@+cos^3@)

=sin^[email protected]^2@

hence LHS=RHS

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