Advertisements
Advertisements
प्रश्न
If `sec θ = 41/40`, then find values of sin θ, cot θ, cosec θ.
Advertisements
उत्तर
`sec θ = 41/40` ...[Given]
∴ `cos θ = 1/(secθ) = 1/(41/40)`
∴ `cos θ = 40/41`
We know that,
sin2θ + cos2θ = 1
∴ `sin^2θ + (40/41)^2 = 1`
∴ `sin^2θ + 1600/1681 = 1`
∴ `sin^2θ = 1 - 1600/1681`
∴ `sin^2θ = (1681- 1600)/1681`
∴ `sin^2θ = 81/1681`
∴ `sin θ = 9/41` ...[Taking square root of both sides]
Now, cosec θ = `1/(sinθ)`
= `1/((9/41))`
= `41/9`
`cot θ = (cosθ)/(sinθ)`
= `((40/41))/((9/41))`
= `40/9`
∴ `sin θ = 9/41, cot θ = 40/9`, cosec θ = `41/9`
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 identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.
As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.
Prove that `(tan^2 theta)/(sec theta - 1)^2 = (1 + cos theta)/(1 - cos theta)`
Without using trigonometric tables evaluate
`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80^@)`
Prove the following trigonometric identities.
`(1 + cos A)/sin^2 A = 1/(1 - cos A)`
Prove the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`
Prove the following trigonometric identities.
`(cosec A)/(cosec A - 1) + (cosec A)/(cosec A = 1) = 2 sec^2 A`
Prove the following identities:
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
`sin^6 theta + cos^6 theta =1 -3 sin^2 theta cos^2 theta`
If `cos B = 3/5 and (A + B) =- 90° ,`find the value of sin A.
`If sin theta = cos( theta - 45° ),where theta " is acute, find the value of "theta` .
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
If m = a secA + b tanA and n = a tanA + b secA , prove that m2 - n2 = a2 - b2
Without using trigonometric identity , show that :
`sin42^circ sec48^circ + cos42^circ cosec48^circ = 2`
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.
If (sin α + cosec α)2 + (cos α + sec α)2 = k + tan2α + cot2α, then the value of k is equal to
Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`
If 2 cos θ + sin θ = `1(θ ≠ π/2)`, then 7 cos θ + 6 sin θ is equal to ______.
