Advertisements
Advertisements
Question
`If sin theta = cos( theta - 45° ),where theta " is acute, find the value of "theta` .
Advertisements
Solution
𝑊𝑒 ℎ𝑎𝑣𝑒,
Sin 𝜃 = cos(𝜃 − 45°)
⟹ cos(90° − 𝜃) = cos(𝜃 − 45°)
Comparing both sides, we get
` 90° - theta = theta - 45°`
` ⇒ theta + theta = 90° + a=45°`
`⇒ 2 theta = 135°`
`⇒ theta = ((135)/2)^°`
∴ 𝜃 = 67.5°
APPEARS IN
RELATED QUESTIONS
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA "cosec" A + 1`
Prove that:
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
`{1/((sec^2 theta- cos^2 theta))+ 1/((cosec^2 theta - sin^2 theta))} ( sin^2 theta cos^2 theta) = (1- sin^2 theta cos ^2 theta)/(2+ sin^2 theta cos^2 theta)`
If tan A = n tan B and sin A = m sin B , prove that `cos^2 A = ((m^2-1))/((n^2 - 1))`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identity :
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
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 α + cosec α)2 + (cos α + sec α)2 = k + tan2α + cot2α, then the value of k is equal to
tan (90 – θ) = ?
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ.
Prove that `sec^2A - "cosec"^2A = (2sin^2A - 1)/(sin^2A *cos^2A)`.
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.
