Advertisements
Advertisements
प्रश्न
Evaluate:
`(cos3"A" – 2cos4"A")/(sin3"A" + 2sin4"A")` , when A = 15°
उत्तर
Given that A= 15°
`(cos 3"A" – 2 cos 4"A")/(sin 3"A" + 2 sin 4"A")`
`= (cos 3 (15°) – 2 cos 4 (15°))/(sin 3 (15°) + 2 sin 4 (15°))`
= `(cos 45° – 2 cos 60°)/(sin 45° + 2 sin 60°)`
= `(1/(sqrt2) – 2 (1/2))/(1/(sqrt2)+2 (sqrt3/2)`
= `(1/(sqrt2) – 1)/(1/(sqrt2)+ sqrt3)`
`= ((1 - sqrt2)/sqrt2)/((1 + sqrt6)/sqrt2)`
= `(1 – sqrt2)/(1+ sqrt6)`
APPEARS IN
संबंधित प्रश्न
If tan (A + B) = `sqrt3` and tan (A – B) = `1/sqrt3`; 0° < A + B ≤ 90°; A > B, find A and B.
Evaluate the following:
2tan2 45° + cos2 30° − sin2 60°
Evaluate the following:
`(5cos^2 60° + 4sec^2 30° - tan^2 45°)/(sin^2 30° + cos^2 30°)`
State whether the following is true or false. Justify your answer.
sinθ = cosθ for all values of θ.
State whether the following are true or false. Justify your answer.
cot A is not defined for A = 0°.
Evaluate the following:
`(sin 20^@)/(cos 70^@)`
Evaluate the following
`sec 11^@/(cosec 79^@)`
Evaluate the following :
`tan 35^@/cot 55^@ + cot 78^@/tan 12^@ -1`
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
tan 65° + cot 49°
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
cosec 54° + sin 72°
Express cos 75° + cot 75° in terms of angles between 0° and 30°.
If Sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A =?
Evaluate: Cosec (65 + θ) – sec (25 – θ) – tan (55 – θ) + cot (35 + θ)
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
cot65° + tan49°
If A = B = 45° ,
show that:
sin (A - B) = sin A cos B - cos A sin B
If tan (A + B) = 1 and tan(A-B)`=1/sqrt3` , 0° < A + B < 90°, A > B, then find the values of A and B.
prove that:
tan (2 x 30°) = `(2 tan 30°)/(1– tan^2 30°)`
Without using tables, evaluate the following: sec30° cosec60° + cos60° sin30°.
Find the value of x in the following: `2sin x/(2)` = 1
Find the value of x in the following: cos2x = cos60° cos30° + sin60° sin30°
If A = 30° and B = 60°, verify that: `(sin("A" -"B"))/(sin"A" . sin"B")` = cotB - cotA
If sin(A - B) = sinA cosB - cosA sinB and cos(A - B) = cosA cosB + sinA sinB, find the values of sin15° and cos15°.
If tan(A - B) = `(1)/sqrt(3)` and tan(A + B) = `sqrt(3)`, find A and B.
If sin(A - B) = `(1)/(2)` and cos(A + B) = `(1)/(2)`, find A and B.
Prove the following:
`(sqrt(3) + 1) (3 - cot 30^circ)` = tan3 60° – 2 sin 60°
The value of cos1°. cos2°. cos3°. cos4°....................... cos90° is ______.
Evaluate: `(5cos^2 60° + 4sec^2 30° - tan^2 45°)/(sin^2 30° + sin^2 60°)`
