Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Advertisements
उत्तर
We have to prove `(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
We know that, `sin^2 theta + cos^2 theta = 1`
Multiplying both numerator and denominator by `(1 + cos theta)`, we have
`(1 - cos theta)/sin theta = ((1 - cos theta)(1 + cos theta))/(sin theta(1 + cos theta))`
`= (1 - cos^2 theta)/(sin theta(1 + cos theta))`
` = (sin^2 theta)/(sin theta(1 + cos theta))`
`= sin theta/(1 + cos theta)`
APPEARS IN
संबंधित प्रश्न
Prove that `cosA/(1+sinA) + tan A = secA`
Prove the following trigonometric identities.
tan2θ cos2θ = 1 − cos2θ
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
If sec A + tan A = p, show that:
`sin A = (p^2 - 1)/(p^2 + 1)`
`(1-cos^2theta) sec^2 theta = tan^2 theta`
If `cos theta = 7/25 , "write the value of" ( tan theta + cot theta).`
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
If cos (\[\alpha + \beta\]= 0 , then sin \[\left( \alpha - \beta \right)\] can be reduced to
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)`
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
If `sec θ + tan θ = sqrt(3)`, complete the activity to find the value of sec θ – tan θ.
Activity:
`square = 1 + tan^2θ` ...[Fundamental trigonometric identity]
`square - tan^2θ = 1`
`(sec θ + tan θ) . (sec θ - tan θ) = square`
`sqrt(3) . (sec θ - tan θ) = 1`
`(sec θ - tan θ) = square`
Prove that `1/("cosec" θ - cot θ) = "cosec" θ + cot θ`.
If 1 + sin2θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
