Advertisements
Advertisements
प्रश्न
cosec4 θ − cosec2 θ = cot4 θ + cot2 θ
Prove the following:
cosec4 θ − cosec2 θ = cot2 θ + cot4 θ
Advertisements
उत्तर १
LHS = cosec4 θ − cosec2 θ
LHS = cosec2 θ (cosec2 θ − 1)
LHS = (cot2 θ + 1)cot2 θ ...`{(cot^2 θ + 1 = cosec^2 θ),(∵ cot^2 θ = cosec^2 θ - 1):}`
LHS = cot4 θ + cot2 θ
RHS = cot4 θ + cot2 θ
RHS = LHS
Hence proved.
उत्तर २
RHS = cot4 θ + cot2 θ
RHS = cot2 θ (cot2 θ + 1)
RHS = (cosec2 θ − 1)cosec2 θ ...`{(cot^2 θ + 1=cosec^2 θ),(∵ cot^2θ = cosec^2 θ - 1):}`
RHS = cosec4 θ − cosec2 θ
LHS = cosec4 θ − cosec2 θ
RHS = LHS
Hence proved.
APPEARS IN
संबंधित प्रश्न
Prove that ` \frac{\sin \theta -\cos \theta +1}{\sin\theta +\cos \theta -1}=\frac{1}{\sec \theta -\tan \theta }` using the identity sec2 θ = 1 + tan2 θ.
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identity :
`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`
Find the value of ( sin2 33° + sin2 57°).
Prove that `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ)) = 1/(tan θ + cot 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)`.
Prove the following identities.
`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ
If 1 + sin2θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.
sin(45° + θ) – cos(45° – θ) is equal to ______.
