Advertisements
Advertisements
Question
Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`
Advertisements
Solution
`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
RELATED QUESTIONS
Prove the following identities:
`(1 + sin A)/(1 - sin A) = (cosec A + 1)/(cosec A - 1)`
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`cos 63^circ sec(90^circ - θ) = 1`
Prove that `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`
