Advertisements
Advertisements
प्रश्न
Evaluate the following: `((1 - cosθ)(1 + cosθ))/((1 - sinθ)(1 + sinθ)` if θ = 30°
Advertisements
उत्तर
θ = 30°
`((1 - cosθ)(1 + cosθ))/((1 - sinθ)(1 + sinθ)`
= `(1 - cos^2θ)/(1 - sin^2 θ)`
= `(1 - cos^2 30°)/(1 - sin^2 30°)`
= `(1 - (sqrt(3)/2)^2)/(1 - (1/2)^2`
= `( 1 - 3/4)/(1 - 1/4)`
= `(1/4)/(3/4)`
= `(1)/(3)`.
APPEARS IN
संबंधित प्रश्न
Solve for x : sin2 x + sin2 30° = 1
Find the value of 'A', if 2 sin 2A = 1
If θ = 30°, verify that: 1 - sin 2θ = (sinθ - cosθ)2
In right-angled triangle ABC; ∠B = 90°. Find the magnitude of angle A, if:
a. AB is `sqrt(3)` times of BC.
B. BC is `sqrt(3)` times of BC.
Evaluate the following: sin(35° + θ) - cos(55° - θ) - tan(42° + θ) + cot(48° - θ)
Evaluate the following: `(3sin37°)/(cos53°) - (5"cosec"39°)/(sec51°) + (4tan23° tan37° tan67° tan53°)/(cos17° cos67° "cosec"73° "cosec"23°)`
Evaluate the following: `(3sin^2 40°)/(4cos^2 50°) - ("cosec"^2 28°)/(4sec^2 62°) + (cos10° cos25° cos45° "cosec"80°)/(2sin15° sin25° sin45° sin65° sec75°)`
If tan4θ = cot(θ + 20°), find the value of θ if 4θ is an acute angle.
If sin(θ - 15°) = cos(θ - 25°), find the value of θ if (θ-15°) and (θ - 25°) are acute angles.
Prove the following: sin58° sec32° + cos58° cosec32° = 2
