Advertisements
Advertisements
प्रश्न
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
Advertisements
उत्तर
Given: sinθ = `11/61`
We know that,
sin2θ + cos2θ = 1
∴ `(11/61)^2 + cos^2θ` = 1
∴ `121/3721 + cos^2θ` = 1
∴ cos2θ = `1 - 121/3721`
∴ cos2θ = `(3721 - 121)/3721`
∴ cos2θ = `3600/3721`
∴ cosθ = `60/61` .......[Taking square root of both sides]
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
Prove the following trigonometric identities.
(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
Prove the following identities:
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
`(1+ cos theta)(1- costheta )(1+cos^2 theta)=1`
If 5x = sec ` theta and 5/x = tan theta , " find the value of 5 "( x^2 - 1/( x^2))`
sec4 A − sec2 A is equal to
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Prove the following identity :
`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`
Prove the following identity :
`(sec^2θ - sin^2θ)/tan^2θ = cosec^2θ - cos^2θ`
If m = a secA + b tanA and n = a tanA + b secA , prove that m2 - n2 = a2 - b2
If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
Prove that: sin6θ + cos6θ = 1 - 3sin2θ cos2θ.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)) + sqrt((1 - sin theta)/(1 + sin theta))` = 2 sec θ
Prove that `"cosec" θ xx sqrt(1 - cos^2theta)` = 1
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S = `square`
= `square/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/square`
= `1/(sintheta*costheta)` ......`[cos^2theta + sin^2theta = square]`
= `1/sintheta xx 1/square`
= `square`
= R.H.S
Prove that sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ
Prove the following trigonometry identity:
(sin θ + cos θ)(cosec θ – sec θ) = cosec θ ⋅ sec θ – 2 tan θ
