Advertisements
Advertisements
प्रश्न
If cos θ = `24/25`, then sin θ = ?
उत्तर
cos θ = `24/25` ......[Given]
We know that,
sin2θ + cos2θ = 1
∴ `sin^2theta + (24/25)^2` = 1
∴ `sin^2theta + 576/625` = 1
∴ sin2θ = `1 - 576/625`
∴ sin2θ = `(625 - 576)/625`
∴ sin2θ = `49/625`
∴ sin θ = `7/25` ......[Taking square root of both sides]
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) 2 (sin^6 θ + cos^6 θ) –3(sin^4 θ + cos^4 θ) + 1 = 0`
`(ii) (sin^8 θ – cos^8 θ) = (sin^2 θ – cos^2 θ) (1 – 2sin^2 θ cos^2 θ)`
Prove the following trigonometric identities.
`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`
Prove the following trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = sec A + tan A`
`cot^2 theta - 1/(sin^2 theta ) = -1`a
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec 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 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
If cos (\[\alpha + \beta\]= 0 , then sin \[\left( \alpha - \beta \right)\] can be reduced to
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove the following identity :
`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq
Prove the following identity :
`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`
Prove the following identity :
`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`
Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
Choose the correct alternative:
`(1 + cot^2"A")/(1 + tan^2"A")` = ?
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ
If cos A + cos2A = 1, then sin2A + sin4 A = ?
Show that `(cos^2(45^circ + theta) + cos^2(45^circ - theta))/(tan(60^circ + theta) tan(30^circ - theta))` = 1
Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.
