Advertisements
Advertisements
प्रश्न
If ` cot A= 4/3 and (A+ B) = 90° ` ,what is the value of tan B?
उत्तर
We have ,
`cot A = 4/3`
⇒ ` cot (90° - B ) = 4/3 (As , A+ B = 90° )`
∴ tanB = `4/3`
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) (sinθ + cosecθ)^2 + (cosθ + secθ)^2 = 7 + tan^2 θ + cot^2 θ`
`(ii) (sinθ + secθ)^2 + (cosθ + cosecθ)^2 = (1 + secθ cosecθ)^2`
`(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`sqrt((1+sinA)/(1-sinA)) = secA + tanA`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA ` using the identity cosec2 A = 1 cot2 A.
Prove the following trigonometric identities.
`cosec theta sqrt(1 - cos^2 theta) = 1`
If sin θ + cos θ = x, prove that `sin^6 theta + cos^6 theta = (4- 3(x^2 - 1)^2)/4`
If sin A + cos A = m and sec A + cosec A = n, show that : n (m2 – 1) = 2 m
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
Write the value of `(1 - cos^2 theta ) cosec^2 theta`.
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
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 :
`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`
Without using trigonometric identity , show that :
`cos^2 25^circ + cos^2 65^circ = 1`
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.
a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to
Prove that
sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`