Advertisements
Advertisements
प्रश्न
Find x , if `cos(2x - 6) = cos^2 30^circ - cos^2 60^circ`
उत्तर
`cos(2x - 6) = cos^2 30^circ - cos^2 60^circ`
⇒ `cos(2x - 6) = cos^2 (90^circ - 60^circ) - cos^2 60^circ`
⇒ `cos(2x - 6) = sin^2 60^circ - cos^2 60^circ`
⇒ `cos(2x - 6) = 1 - 2cos^2 60^circ = 1 - 2(1/2)^2 = 1 - 1/2 = 1/2`
⇒ `cos(2x - 6) = 1/2`
⇒ `cos(2x - 6) = cos60^circ`
⇒ `(2x - 6) = 60^circ`
⇒ `2x = 66^circ`
⇒ `x = 33^circ`
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`
[Hint: Write the expression in terms of sinθ and cosθ]
Prove the following trigonometric identities.
`cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)`
`(sec^2 theta -1)(cosec^2 theta - 1)=1`
Prove the following identity :
`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle.
If cos (α + β) = 0, then sin (α – β) can be reduced to ______.
If 1 + sin2θ = 3sinθ cosθ, then prove that tanθ = 1 or `1/2`.
Eliminate θ if x = r cosθ and y = r sinθ.
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
