Advertisements
Advertisements
प्रश्न
If `tan θ = 9/40`, complete the activity to find the value of sec θ.
Activity:
sec2θ = 1 + `square` ...[Fundamental trigonometric identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square`
sec θ = `square`
Advertisements
उत्तर
sec2θ = 1 + \[\boxed{\text{tan}^2θ}\] ...[Fundamental trigonometric identity]
∴ sec2θ = 1 + \[\boxed{\frac{9}{40}}^2\]
∴ sec2θ = 1 + \[\boxed{\frac{81}{1600}}\]
∴ sec2θ = `1681/1600`
∴ sec θ = \[\boxed{\frac{41}{40}}\]
संबंधित प्रश्न
Prove the following trigonometric identities:
(1 + cot2 A) sin2 A = 1
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
Prove the following trigonometric identities
If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2
Prove the following trigonometric identities.
if x = a cos^3 theta, y = b sin^3 theta` " prove that " `(x/a)^(2/3) + (y/b)^(2/3) = 1`
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m2 – n2 = a2 – b2
Prove the following identities:
`cosecA - cotA = sinA/(1 + cosA)`
Prove the following identities:
`(1 + cos theta - sin^2 theta )/(sin theta (1 + cos theta)) = cot theta`
Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`
Simplify : 2 sin30 + 3 tan45.
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identity :
`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
If cosθ + sinθ = `sqrt2` cosθ, show that cosθ - sinθ = `sqrt2` sinθ.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
If `sqrt(3)` sin θ – cos θ = θ, then show that tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`
Prove that sec2θ – cos2θ = tan2θ + sin2θ.
