Advertisements
Advertisements
प्रश्न
If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.
Advertisements
उत्तर
sin θ + cos θ = `sqrt(3)`
Squaring on both sides:
(sin θ + cos θ)2 = `(sqrt(3))^2`
sin2 θ + cos2 θ + 2 sin θ cos θ = 3
1 + 2 sin θ cos θ = 3
2 sin θ cos θ = 3 – 1
2 sin θ cos θ = 2
∴ sin θ cos θ = 1
L.H.S = tan θ + cot θ
= `sin theta/cos theta + cos theta/sin theta`
= `(sin^2 theta + cos^2 theta)/(sin theta cos theta)`
= `1/(sin theta cos theta)`
= `1/1` ...(sin θ cos θ = 1)
= 1 = R.H.S.
⇒ tan θ + cot θ = 1
L.H.S = R.H.S
APPEARS IN
संबंधित प्रश्न
If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p2 – 1) = 2p
Prove that `(tan^2 theta)/(sec theta - 1)^2 = (1 + cos theta)/(1 - cos theta)`
Prove the following trigonometric identities.
`((1 + tan^2 theta)cot theta)/(cosec^2 theta) = tan theta`
Prove the following trigonometric identity:
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
Without using trigonometric table , evaluate :
`cosec49°cos41° + (tan31°)/(cot59°)`
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
Prove that sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A.
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
