Advertisements
Advertisements
प्रश्न
Without using tables, evaluate the following: cosec245° sec230° - sin230° - 4cot245° + sec260°.
उत्तर
cosec245° sec230° - sin230° - 4cot245° + sec260°.
sin45° = `(1)/sqrt(2)`
cosec45° = `sqrt(2)/(1)`
sin30° = `(1)/(2)` = cos60°
sec60° = 2
cos30° = `sqrt(3)/(2)`
sec30° = `(2)/sqrt(3)`
tan45° = 1
cot45° = 1
cosec245° sec230° - sin230° - 4cot245° + sec260°
= `(sqrt(2)/1)^2 (2/sqrt(3))^2 - (1/2)^2 - 4(1)^2 + (2)^2`
= `2 xx (4)/(3) - (1)/(4) - 4 + 4`
= `(8)/(3) - (1)/(4)`
= `(32 - 3)/(12)`
= `(29)/(12)`.
APPEARS IN
संबंधित प्रश्न
If x = 30°, verify that
(i) `\tan 2x=\frac{2\tan x}{1-\tan ^{2}x`
(ii) `\sin x=\sqrt{\frac{1-\cos 2x}{2}}`
Evaluate the following:
2tan2 45° + cos2 30° − sin2 60°
sin 2A = 2 sin A is true when A = ______.
State whether the following is true or false. Justify your answer.
The value of cos θ increases as θ increases.
State whether the following is true or false. Justify your answer.
sinθ = cosθ for all values of θ.
Evaluate the following :
`(sin 21^@)/(cos 69^@)`
Evaluate the following :
`tan 10^@/cot 80^@`
Evaluate the following :
`((sin 27^@)/(cos 63^@))^2 - (cos 63^@/sin 27^@)^2`
If A, B, C are the interior angles of a triangle ABC, prove that
`tan ((C+A)/2) = cot B/2`
Prove that sin 48° sec 42° + cos 48° cosec 42° = 2
Prove the following :
`(cos(90°−A) sin(90°−A))/tan(90°−A) - sin^2 A = 0`
Evaluate tan 35° tan 40° tan 50° tan 55°
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
cot65° + tan49°
If sin x = cos x and x is acute, state the value of x
If `sqrt3` = 1.732, find (correct to two decimal place) the value of sin 60o
find the value of: sin2 30° + cos2 30°+ cot2 45°
Prove that:
`((tan60° + 1)/(tan 60° – 1))^2 = (1+ cos 30°) /(1– cos 30°) `
If `sqrt3` = 1.732, find (correct to two decimal place) the value of `(2)/(tan 30°)`
If A = 30o, then prove that :
2 cos2 A - 1 = 1 - 2 sin2A
If A = 30°;
show that:
(sinA - cosA)2 = 1 - sin2A
If A = 30°;
show that:
`(1 – cos 2"A")/(sin 2"A") = tan"A"`
Without using tables, evaluate the following: 4(sin430° + cos460°) - 3(cos245° - sin290°).
Without using tables, find the value of the following: `(sin30°)/(sin45°) + (tan45°)/(sec60°) - (sin60°)/(cot45°) - (cos30°)/(sin90°)`
If sin(A - B) = sinA cosB - cosA sinB and cos(A - B) = cosA cosB + sinA sinB, find the values of sin15° and cos15°.
Find the value of the following:
(sin 90° + cos 60° + cos 45°) × (sin 30° + cos 0° – cos 45°)
If sin 30° = x and cos 60° = y, then x2 + y2 is
If 2 sin 2θ = `sqrt(3)` then the value of θ is
If sin(A + B) = 1 and cos(A – B)= `sqrt(3)/2`, 0° < A + B ≤ 90° and A > B, then find the measures of angles A and B.
