Advertisements
Advertisements
प्रश्न
Evaluate the following: `((sin3θ - 2sin4θ))/((cos3θ - 2cos4θ))` when 2θ = 30°
Advertisements
उत्तर
2θ = 30°
⇒ θ = 15°
∴ `(sin3θ - 2sin4θ)/(cos3θ - 2cos4θ)`
= `(sin3 xx 15° - 2sin4 xx 15°)/(cos3 xx 15° - 2cos"4 xx 15°)`
= `"(sin45° - 2sin60°)/(cos45° - 2cos60°)`
= `(1/sqrt(2) - 2 xx sqrt(3)/(2))/((1)/sqrt(2) - 2 xx (1)/(2))`
= `(1/sqrt(2) - sqrt(3))/(1/sqrt(2) - 1)`
= `((1 - sqrt(6))/(sqrt(2)))/((1 - sqrt(2))/(sqrt(2)`
= `(1 - sqrt(6))/(1 - sqrt(2))`
= `(1 - sqrt(6))/(1 - sqrt(2)) xx (1 + sqrt(2))/(1 + sqrt(2)`
= `(1 + sqrt(2) - sqrt(6) - sqrt12)/(1 - 2)`
= `(1 + sqrt(2) - sqrt(6) - 2sqrt(3))/(-1)`
= `2sqrt(3) + sqrt(6) - sqrt(2) - 1`.
APPEARS IN
संबंधित प्रश्न
From the given figure,
find:
(i) cos x°
(ii) x°
(iii) `(1)/(tan^2 xx°) – (1)/(sin^2xx°)`
(iv) Use tan xo, to find the value of y.
Calculate the value of A, if (sec 2A - 1) (cosec 3A - 1) = 0
Solve for x : cos2 30° + sin2 2x = 1
If `sqrt(2) = 1.414 and sqrt(3) = 1.732`, find the value of the following correct to two decimal places tan60°
Evaluate the following: `((1 - cosθ)(1 + cosθ))/((1 - sinθ)(1 + sinθ)` if θ = 30°
In the given figure, if tan θ = `(5)/(13), tan α = (3)/(5)` and RS = 12m, find the value of 'h'.
The perimeter of a rhombus is 100 cm and obtuse angle of it is 120°. Find the lengths of its diagonals.
In the given figure; ∠B = 90°, ∠ADB = 30°, ∠ACB = 45° and AB = 24 m. Find the length of CD.
Evaluate the following: `(sin25° cos43°)/(sin47° cos 65°)`
Evaluate the following: `(2sin28°)/(cos62°) + (3cot49°)/(tan41°)`
