Advertisements
Advertisements
प्रश्न
Write the value of `4 tan^2 theta - 4/ cos^2 theta`
Advertisements
उत्तर
4 `tan^2 theta - 4 / cos^2 theta`
=` 4 tan^2 theta - 4 sec^2 theta`
=`4 (tan^2 theta - sec^2 theta )`
=4(-1)
= -4
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(1+ secA)/sec A = (sin^2A)/(1-cosA)`
[Hint : Simplify LHS and RHS separately.]
Prove the following trigonometric identities.
`(1 + cos θ + sin θ)/(1 + cos θ - sin θ) = (1 + sin θ)/cos θ`
Prove the following identities:
`1/(tan A + cot A) = cos A sin A`
Show that : `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec A cosec A`
If `(cot theta ) = m and ( sec theta - cos theta) = n " prove that " (m^2 n)(2/3) - (mn^2)(2/3)=1`
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
Find the value of sin 30° + cos 60°.
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
Prove the following identities.
`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2
If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.
Choose the correct alternative:
sec 60° = ?
If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
If 2sin2θ – cos2θ = 2, then find the value of θ.
