Advertisements
Advertisements
Question
If tan θ = `7/24`, then to find value of cos θ complete the activity given below.
Activity:
sec2θ = 1 + `square` ......[Fundamental tri. identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square/576`
sec2θ = `square/576`
sec θ = `square`
cos θ = `square` .......`[cos theta = 1/sectheta]`
Advertisements
Solution
sec2θ = 1 + tan2θ ......[Fundamental tri. identity]
∴ sec2θ = 1 + `(7/24)^2`
∴ sec2θ = 1 + `49/576`
∴ sec2θ =`(576 + 49)/576`
∴ sec2θ = `625/576`
∴ sec θ = `25/24`
∴ cos θ = `24/25` .......`[cos theta = 1/sectheta]`
RELATED QUESTIONS
If m=(acosθ + bsinθ) and n=(asinθ – bcosθ) prove that m2+n2=a2+b2
Prove the following identities:
(1 – tan A)2 + (1 + tan A)2 = 2 sec2A
Prove the following identities:
cosec4 A – cosec2 A = cot4 A + cot2 A
Prove the following identities:
`(secA - tanA)/(secA + tanA) = 1 - 2secAtanA + 2tan^2A`
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
Prove that:
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`
Show that none of the following is an identity:
`sin^2 theta + sin theta =2`
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identity :
`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
Without using trigonometric table , evaluate :
`(sin47^circ/cos43^circ)^2 - 4cos^2 45^circ + (cos43^circ/sin47^circ)^2`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
Prove that `(cos^2theta)/(sintheta) + sintheta` = cosec θ
Prove that sec2θ – cos2θ = tan2θ + sin2θ
If cos A + cos2A = 1, then sin2A + sin4 A = ?
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
If 2sin2θ – cos2θ = 2, then find the value of θ.
