Advertisements
Advertisements
प्रश्न
What is the value of (1 + tan2 θ) (1 − sin θ) (1 + sin θ)?
Advertisements
उत्तर
We have,
`(1+tan^2θ)(1-sinθ)(1+sin θ)=(1+tan ^2 θ){(1-sinθ)(1+sinθ)}`
= `(1+tan^2θ)(1-sin^2θ)`
We know that,
`sec^2θ-tan^2θ=1`
⇒ `sec^2 θ=1+tan^2θ`
`sin^2 θ+cos ^2θ=1`
⇒ `cos^2 θ=1sin^2θ`
Therefore,
`(1+tan^2θ)(1-sin θ)(1+sin θ) = sec^2 θ xxcos^2θ`
= `1/cos^2θ xx cos^2 θ`
=` 1`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`tan theta - cot theta = (2 sin^2 theta - 1)/(sin theta cos theta)`
Prove the following trigonometric identities.
(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A
Prove the following identities:
`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
`(sec^2 theta -1)(cosec^2 theta - 1)=1`
Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`
Write the value of`(tan^2 theta - sec^2 theta)/(cot^2 theta - cosec^2 theta)`
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
Prove the following identity:
`cosA/(1 + sinA) = secA - tanA`
Prove the following identity :
`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a2 – 1) is equal to
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S. = `square`
= `square/(sinθ) + (sinθ)/(cosθ)`
= `(cos^2θ + sin^2θ)/square`
= `1/(sinθ.cosθ)` ...`[cos^2θ + sin^2θ = square]`
= `1/(sinθ) xx 1/square`
= `square`
= R.H.S.
Prove that `(1 + sec A)/(sec A) = (sin^2A)/(1 - cos A)`.
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
Show that tan4θ + tan2θ = sec4θ – sec2θ.
