Question

Prove that Sin0(1+tan0) +cos0(1+cot0)=Sec0+ cosec0.

Answer 1

To prove Sin0(1+tan0) + cos0(1+cot0)=sec0+cosec0

Taking LHS = Sin0(1+tan0) +cos0(1+cot0)

=sin0+sin0×tan0 +cos0+cos0×cot0

= sin0+ sin20/cos0 +cos0+cos2/sin0

=(sin0xcos0+sin20)/cos0+(cos0×sin0+cos20)/sin0

= (sin20(cos0+sin0)+cos20(sin0+cos0)/sin0×cos0

=sin2cos0+sin30+cos20+sino+cos30)/sin0xcos0

=(sin2cos0+cos30+cos2sin0+sin30)/sin0×cos0

=(cos0(sin20+cos20)+sin0(cos20+sin20)/sin0xcos0

=(cos0×1 + sin0×1)/sin0×cos0

=cos0/sino×cos0 + sin0/sin0×cos0

=1/sin0 + 1/cos0

=cosec0 + sec0

= sec0 + cosec0 = RHS

Hence proved

Answer 2

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