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 trigonometric identities.
`(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`
If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`.
What is the value of \[6 \tan^2 \theta - \frac{6}{\cos^2 \theta}\]
Prove the following identity :
`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq
If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.
Prove that `(cot "A" + "cosec A" - 1)/(cot "A" - "cosec A" + 1) = (1 + cos "A")/sin "A"`
sin2θ + sin2(90 – θ) = ?
Prove that `(sec A)/(tan A + cot A) = sin A`.
If cos A + cos2A = 1, then sin2A + sin4A = ?
`(cos^2 θ)/(sin^2 θ) - 1/(sin^2 θ)`, in simplified form, is ______.
