Advertisements
Advertisements
Question
If tanθ `= 3/4` then find the value of secθ.
Advertisements
Solution
If tanθ = 34
1 + tan2θ = sec2θ
∴ 1 + `(3/4)^2= sec^2θ`
∴ `1 + 9/16 = sec^2θ`
∴ `25/16 = sec^2θ`
∴ `secθ = 5/4`
APPEARS IN
RELATED QUESTIONS
Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`
[Hint: Write the expression in terms of sinθ and cosθ]
If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.
Prove the following trigonometric identities.
`(1 - sin θ)/(1 + sin θ) = (sec θ - tan θ)^2`
Prove the following trigonometric identities.
`(1 + cos A)/sin^2 A = 1/(1 - cos A)`
Prove the following trigonometric identities.
`(1 - tan^2 A)/(cot^2 A -1) = tan^2 A`
Prove the following trigonometric identities.
`1 + cot^2 theta/(1 + cosec theta) = cosec theta`
if `x/a cos theta + y/b sin theta = 1` and `x/a sin theta - y/b cos theta = 1` prove that `x^2/a^2 + y^2/b^2 = 2`
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
Write the value of `(cot^2 theta - 1/(sin^2 theta))`.
Prove that:
`"tanθ"/("secθ" – 1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`
(sec A + tan A) (1 − sin A) = ______.
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
If sin θ = `1/2`, then find the value of θ.
Prove that tan2Φ + cot2Φ + 2 = sec2Φ.cosec2Φ.
Prove that sec2 (90° - θ) + tan2 (90° - θ) = 1 + 2 cot2 θ.
If x sin3θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ , then show that x2 + y2 = 1.
Without using the trigonometric table, prove that
cos 1°cos 2°cos 3° ....cos 180° = 0.
Prove that `(sin θ + "cosec" θ)/(sin θ) = 2 + cot^2θ`.
Prove that `(1 + sec A)/(sec A) = (sin^2A)/(1 - cos A)`.
