Advertisements
Advertisements
प्रश्न
Prove that `(sin^2θ)/(cos θ) + cos θ = sec θ`.
Advertisements
उत्तर
L.H.S. = `(sin^2θ)/(cos θ) + cos θ`
= `(sin^2θ + cos^2θ)/(cos θ)`
= `1/(cos θ)` ...[∵ sin2θ + cos2θ = 1]
= sec θ
= R.H.S.
∴ `(sin^2θ)/(cos θ) + cos θ = sec θ`
APPEARS IN
संबंधित प्रश्न
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
Prove the following trigonometric identities.
`"cosec" theta sqrt(1 - cos^2 theta) = 1`
Prove the following trigonometric identities.
`(1 - tan^2 A)/(cot^2 A -1) = tan^2 A`
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
Prove the following trigonometric identities.
(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)
Prove the following trigonometric identities
If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2
If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, show that `x^2/a^2 + y^2/b^2 - x^2/c^2 = 1`
(i)` (1-cos^2 theta )cosec^2theta = 1`
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
Show that none of the following is an identity:
`sin^2 theta + sin theta =2`
Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`
If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2.
If sec θ + tan θ = x, then sec θ =
Prove the following identity :
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`
There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.
If tan A + sin A = m and tan A − sin A = n, then show that `m^2 - n^2 = 4 sqrt (mn)`.
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
