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प्रश्न
Solve the following equation: `(cos θ)/(1 - sin θ) + cos θ/(1 + sinθ) = 4`.
उत्तर
We have,
∴ `(cos θ)/(1 - sin θ) + (cos θ)/(1 + sin θ) = 4`
`⇒ cos θ{(1)/(1 - sin θ) + (1)/(1 + sin θ)} = 4`
`⇒ cos θ{(1 + sin θ + 1 - sin θ)/((1 - sin θ)(1 + sin θ))} = 4`
⇒ 2cos θ = 4( 1 - sinθ )( 1 + sin θ)
⇒ 2cos θ = 4( 1 - sin2θ )
⇒ 2 cos θ = 4cos2θ
⇒ 4cos2θ - 2cos θ = 0
⇒ 2cos θ( 2cos θ - 1) = 0
⇒ 2cos θ = 0 or ⇒ 2cos θ - 1 = 0
⇒ cos θ = 0 or ⇒ cos θ = `1/2`
⇒ θ = 60°, (since 0 < θ < 90° ).
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