Question

If sec theta + tan theta = 4 , find sin theta and cos theta

Answer 1

secθ+tanθ=4 ----------------------------(1)
We know that,
sec²θ-tan²θ=1
or, (secθ+tanθ)(secθ-tanθ)=1
or, 4(secθ-tanθ)=1
or, secθ-tanθ=1/4 -----------------------(2)
Adding (1) and (2) we get,
2secθ=4+1/4
or, secθ=(16+1)/8
∴, cosθ=1/secθ=8/17
∴, sinθ=√(1-cos²θ)
or, sinθ=√1-(8/17)²
or, sinθ=√(1-64/289)
or, sinθ=√(289-64)/289
or, sinθ=√225/289
or, sinθ=15/17
∴, sinθ=15/17 and cosθ=8/17