Advertisements
Advertisements
प्रश्न
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
उत्तर
Given:
`cosec^2θ (1+cosθ)(1-cosθ)=λ`
⇒ `cosec^2θ (1+cosθ)(1-cosθ)=λ`
⇒ `cosec^2θ(1-cos^2θ)=λ`
⇒`cosec^θ sin^2θ=λ`
⇒`1/sin^2θxx sin^2θ=λ`
⇒` 1=λ`
⇒`λ=1`
Thus, the value of λ is 1.
APPEARS IN
संबंधित प्रश्न
Evaluate without using trigonometric tables:
`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`
Prove the following trigonometric identities.
`cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A`
Prove the following trigonometric identities
If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2
if `a cos^3 theta + 3a cos theta sin^2 theta = m, a sin^3 theta + 3 a cos^2 theta sin theta = n`Prove that `(m + n)^(2/3) + (m - n)^(2/3)`
Prove the following identities:
`1/(tan A + cot A) = cos A sin A`
Prove that:
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Write the value of `(cot^2 theta - 1/(sin^2 theta))`.
Write the value of tan1° tan 2° ........ tan 89° .
Write the value of cosec2 (90° − θ) − tan2 θ.
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.
Prove that: `1/(sec θ - tan θ) = sec θ + tan θ`.
Prove that: `(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(sin^2 A - cos^2 A)`.
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
If tan θ = `13/12`, then cot θ = ?
Prove that `sec"A"/(tan "A" + cot "A")` = sin A
