prove that
sin theta/sin(90-theta)=sec theta cosec theta.
Anonymous:
But u have prove that tan(angle a+angle b/2)=cot angle c/2
K. I understood. Btw thank u so much.
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sin θ/sin(90- θ) =sin θ/cos θ ....................sin(90- θ)=cos θ
cos θ/cos(90- θ)=cos θ/sin θ.........................cos(90- θ)=sin θ
adding both of these equation and taking lcm
we get
sin^2 θ+cos^2 θ/sin θcos θ
and we know that
sin^2 θ+cos^2 θ=1
now we have
1/sin θcos θ=sec θcosec θ
taking rhs we get
sec θ=1/cos θ and cosec θ=1/sin θ
so
1/sin θcos θ=sec θcosec θ
hence proved
cos θ/cos(90- θ)=cos θ/sin θ.........................cos(90- θ)=sin θ
adding both of these equation and taking lcm
we get
sin^2 θ+cos^2 θ/sin θcos θ
and we know that
sin^2 θ+cos^2 θ=1
now we have
1/sin θcos θ=sec θcosec θ
taking rhs we get
sec θ=1/cos θ and cosec θ=1/sin θ
so
1/sin θcos θ=sec θcosec θ
hence proved
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