sin(90∘−θ)=cos(θ)sin(90^\circ-\theta)=cos(\theta)sin(90∘−θ)=cos(θ)
cos(90∘−θ)=sin(θ)cos(90^\circ-\theta)=sin(\theta)cos(90∘−θ)=sin(θ)
sec(90∘−θ)=1cos(90∘−θ)=1sin(θ)sec (90^\circ-\theta)=\frac{1}{cos(90^\circ-\theta)}=\frac{1}{sin(\theta)}sec(90∘−θ)=cos(90∘−θ)1=sin(θ)1
Cosec(90∘−θ)=1sin(90∘−θ)=1cos(θ)Cosec (90^\circ-\theta)=\frac{1}{sin(90^\circ-\theta)}=\frac{1}{cos(\theta)}Cosec(90∘−θ)=sin(90∘−θ)1=cos(θ)1
sin(90∘−θ)cosec(90∘−θ)+cos(90∘−θ)sec(90∘−θ)=cos(θ)sec(θ)+sin(θ)cosec(θ)=cos(θ)1cos(θ)+sin(θ)1sin(θ)=\frac{sin(90^\circ-\theta)}{cosec(90^\circ-\theta)}+\frac{cos(90^\circ-\theta)}{sec(90^\circ-\theta)}=\frac{cos(\theta)}{sec(\theta)}+\frac{sin(\theta)}{cosec(\theta)}=\frac{cos(\theta)}{\frac{1}{cos(\theta)}}+\frac{sin(\theta)}{\frac{1}{sin(\theta)}}=cosec(90∘−θ)sin(90∘−θ)+sec(90∘−θ)cos(90∘−θ)=sec(θ)cos(θ)+cosec(θ)sin(θ)=cos(θ)1cos(θ)+sin(θ)1sin(θ)=
=cos2(θ)+sin2(θ)=1=cos^2(\theta)+sin^2(\theta)=1=cos2(θ)+sin2(θ)=1
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