Question

If tan theta plus sec theta equals to x Prove that sin theta equals to x square minus one by x square plus one​

Answer 1

Answer:

tanθ+secθ=x

sinθ=x²-1/x²+1

Step-by-step explanation:

• tanθ+secθ=x

• sinθ/cosθ + 1/cosθ = x

• (sinθ+1)/cosθ = x
• now by squaring both the sides ,we get,
• (sinθ+1)²/cos²θ = x²
• sin²θ+1+2sinθ = x²cos²θ
• sin²θ+1+2sinθ = x²(1-sin²θ)
• sin²θ+1+2sinθ = x²- x²sin²θ
• sin²θ(1+x²)+2sinθ+(1-x²) = 0

• here in this quadratic equation, a=1+x²
• b=2
• c=1-x²
• now by formula,
• sinθ= $\frac{-2+or-\sqrt{2^2-4+4x^4} }{2(x^2+1)}$  
• sinθ=x²-1/x²+1 (Ans.)(proved)
• thank u.......
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