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
Find the value of θ in each of the following :
(i) 2 sin 2θ = √3 (ii) 2 cos 3θ = 1
If tan (A + B) = `sqrt3` and tan (A – B) = `1/sqrt3`; 0° < A + B ≤ 90°; A > B, find A and B.
Evaluate the following in the simplest form: sin 60º cos 45º + cos 60º sin 45º
Evaluate the following:
`(sin 30° + tan 45° – cosec 60°)/(sec 30° + cos 60° + cot 45°)`
State whether the following is true or false. Justify your answer.
The value of sinθ 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 20^@)/(cos 70^@)`
Evaluate the following :
`(sin 21^@)/(cos 69^@)`
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
tan 65° + cot 49°
If A, B, C are the interior angles of a triangle ABC, prove that
`tan ((C+A)/2) = cot B/2`
Evaluate: `sin 50^@/cos 40^@ + (cosec 40^@)/sec 50^@ - 4 cos 50^@ cosec 40^@`
Evaluate: `(2sin 68)/cos 22 - (2 cot 15^@)/(5 tan 75^@) - (8 tan 45^@ tan 20^@ tan 40^@ tan 50^@ tan 70^@)/5`
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
sin67° + cos75°
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
cot65° + tan49°
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratios: sin 45°
If A = B = 45° ,
show that:
sin (A - B) = sin A cos B - cos A sin B
find the value of: cosec2 60° - tan2 30°
Prove that:
cos 30° . cos 60° - sin 30° . sin 60° = 0
Prove that:
`((tan60° + 1)/(tan 60° – 1))^2 = (1+ cos 30°) /(1– cos 30°) `
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratio: cos 45°
If A = 30°;
show that:
(sinA - cosA)2 = 1 - sin2A
Without using tables, evaluate the following: cosec330° cos60° tan345° sin290° sec245° cot30°.
Without using tables, evaluate the following: 4(sin430° + cos460°) - 3(cos245° - sin290°).
Prove that: sin60°. cos30° - sin60°. sin30° = `(1)/(2)`
Find the value of x in the following: tan x = sin45° cos45° + sin30°
If A = 30° and B = 60°, verify that: sin (A + B) = sin A cos B + cos A sin B
Find the value of the following:
`(tan45^circ)/("cosec"30^circ) + (sec60^circ)/(cot45^circ) - (5sin90^circ)/(2cos0^circ)`
The value of `(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` is
Prove the following:
`(sqrt(3) + 1) (3 - cot 30^circ)` = tan3 60° – 2 sin 60°
