Advertisements
Advertisements
प्रश्न
Prove that sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ.
Advertisements
उत्तर
L.H.S. = sin θ (1 – tan θ) – cos θ (1 – cot θ)
= `sin θ (1 - (sin θ)/(cos θ)) - cos θ (1 - (cos θ)/(sin θ))`
= `sin θ - (sin^2θ)/(cosθ) - cos θ + (cos^2θ)/(sinθ)`
= `sin θ + (cos^2θ)/(sinθ) - (sin^2θ)/(cosθ) - cos θ`
= `(sin^2θ + cos^2θ)/(sinθ) - ((sin^2θ + cos^2θ)/(cosθ))`
= `1/(sinθ) - 1/(cosθ)` ...[∵ sin2θ + cos2θ = 1]
= cosec θ – sec θ
= R.H.S.
∴ sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ
APPEARS IN
संबंधित प्रश्न
The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
if `a cos^3 theta + 3a cos theta sin^2 theta = m, a sin^3 theta + 3 a cos^2 theta sin theta = n`Prove that `(m + n)^(2/3) + (m - n)^(2/3)`
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
`sin^2 theta + 1/((1+tan^2 theta))=1`
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
`(1+ cos theta - sin^2 theta )/(sin theta (1+ cos theta))= cot theta`
Write the value of `4 tan^2 theta - 4/ cos^2 theta`
If a cot θ + b cosec θ = p and b cot θ − a cosec θ = q, then p2 − q2
Choose the correct alternative:
1 + tan2 θ = ?
Evaluate:
`(tan 65^circ)/(cot 25^circ)`
Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
Prove the following identities.
tan4 θ + tan2 θ = sec4 θ – sec2 θ
Prove that `(sin θ + "cosec" θ)/(sin θ) = 2 + cot^2θ`.
Prove that `(cot A)/(1 - tan A) + (tan A)/(1 - cot A) = 1 + tan A + cot A = sec A . "cosec" A + 1`.
If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
Let x1, x2, x3 be the solutions of `tan^-1((2x + 1)/(x + 1)) + tan^-1((2x - 1)/(x - 1))` = 2tan–1(x + 1) where x1 < x2 < x3 then 2x1 + x2 + x32 is equal to ______.
