Advertisements
Advertisements
प्रश्न
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that a2 + b2 = m2 + n2
Advertisements
उत्तर
R.H.S `m^2 sin^2 theta`
`= (a cos theta + b sin theta)^2 + (a sin theta - b cos theta)^2`
`= a^2 cos^2 theta + b^2 sin^2 theta + 2 ab sin theta cos theta + a^2 sin^2 theta + b^2 cos^2 theta - 2 ab sin theta cos theta`
`= a^2 cos^2 theta + b^2 cos^2 theta + b^2 sin^2 theta + a^2 sin^2 theta`
`= a^2(sin^2 theta + cos^2 theta) + b^2(sin^2 theta + cos^2 theta)`
`=a^2 + b^2` (∵ `sin^2 theta + cos^2 theta = 1`)
APPEARS IN
संबंधित प्रश्न
Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`
Prove the following trigonometric identities.
`cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)`
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
cosec4θ − cosec2θ = cot4θ + cot2θ
If \[\sin \theta = \frac{1}{3}\] then find the value of 9tan2 θ + 9.
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
Prove that :(sinθ+cosecθ)2+(cosθ+ secθ)2 = 7 + tan2 θ+cot2 θ.
If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.
tan θ cosec2 θ – tan θ is equal to
If x = a tan θ and y = b sec θ then
If tan θ = `13/12`, then cot θ = ?
Prove that `(sintheta + tantheta)/cos theta` = tan θ(1 + sec θ)
Prove that `(cos^2theta)/(sintheta) + sintheta` = cosec θ
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
