Advertisements
Advertisements
प्रश्न
`If sin theta = cos( theta - 45° ),where theta " is acute, find the value of "theta` .
Advertisements
उत्तर
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
संबंधित प्रश्न
Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`
`(sec theta -1 )/( sec theta +1) = ( sin ^2 theta)/( (1+ cos theta )^2)`
Show that none of the following is an identity:
`sin^2 theta + sin theta =2`
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
If cosec θ − cot θ = α, write the value of cosec θ + cot α.
Prove the following identity :
`(cos^3θ + sin^3θ)/(cosθ + sinθ) + (cos^3θ - sin^3θ)/(cosθ - sinθ) = 2`
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Without using trigonometric table, prove that
`cos^2 26° + cos 64° sin 26° + (tan 36°)/(cot 54°) = 2`
Prove that: `(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(sin^2 A - cos^2 A)`.
Prove that sin2 5° + sin2 10° .......... + sin2 85° + sin2 90° = `9 1/2`.
Prove the following identities.
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
The value of sin2θ + `1/(1 + tan^2 theta)` is equal to
sin(45° + θ) – cos(45° – θ) is equal to ______.
If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
cosec θ = `41/9`
and sin θ = `1/("cosec" θ)`
sin θ = `1/square`
∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
If sin A = `1/2`, then the value of sec A is ______.
