Advertisements
Advertisements
Question
If tan θ = 2, where θ is an acute angle, find the value of cos θ.
Solution
1 + tan2 θ = sec2 θ
∴ 1 + (2)2 = sec2 θ
∴ sec2 θ = 1 + 4
= 5
sec θ = `sqrt(5)`
cos θ = `1/(sec theta)`
∴ cos θ = `1/sqrt(5)`
APPEARS IN
RELATED QUESTIONS
Prove that:
sec2θ + cosec2θ = sec2θ x cosec2θ
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
Prove the following identities:
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
If tan A = n tan B and sin A = m sin B, prove that:
`cos^2A = (m^2 - 1)/(n^2 - 1)`
`1/((1+ sintheta ))+1/((1- sin theta ))= 2 sec^2 theta`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
cos4 A − sin4 A is equal to ______.
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identity :
`2(sin^6θ + cos^6θ) - 3(sin^4θ + cos^4θ) + 1 = 0`
Prove the following identity :
`[1/((sec^2θ - cos^2θ)) + 1/((cosec^2θ - sin^2θ))](sin^2θcos^2θ) = (1 - sin^2θcos^2θ)/(2 + sin^2θcos^2θ)`
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
Without using trigonometric table , evaluate :
`cosec49°cos41° + (tan31°)/(cot59°)`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
If sin θ = `1/2`, then find the value of θ.
Prove the following identities:
`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.
Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`
Choose the correct alternative:
`(1 + cot^2"A")/(1 + tan^2"A")` = ?
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
Prove the following trigonometry identity:
(sinθ + cosθ)(cosecθ – secθ) = cosecθ.secθ – 2 tanθ
