Advertisements
Advertisements
प्रश्न
If tan θ = 2, where θ is an acute angle, find the value of cos θ.
Advertisements
उत्तर
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
संबंधित प्रश्न
Prove the following trigonometric identities.
`cos theta/(1 + sin theta) = (1 - sin theta)/cos theta`
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following trigonometric identities.
`1 + cot^2 theta/(1 + cosec theta) = cosec theta`
If cos θ + cot θ = m and cosec θ – cot θ = n, prove that mn = 1
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
Write True' or False' and justify your answer the following :
The value of \[\cos^2 23 - \sin^2 67\] is positive .
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
Without using trigonometric identity , show that :
`sin(50^circ + θ) - cos(40^circ - θ) = 0`
Find A if tan 2A = cot (A-24°).
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
Prove that sec θ. cosec (90° - θ) - tan θ. cot( 90° - θ ) = 1.
Prove that `sqrt((1 + sin θ)/(1 - sin θ))` = sec θ + tan θ.
Prove that `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) = 2`.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
Choose the correct alternative:
cos θ. sec θ = ?
tan θ × `sqrt(1 - sin^2 θ)` is equal to:
Prove the following identity:
(sin2θ – 1)(tan2θ + 1) + 1 = 0
