Advertisements
Advertisements
प्रश्न
Find the value of x in the following: tan x = sin45° cos45° + sin30°
उत्तर
tan x = sin45° cos45° + sin30°
⇒ tan x = `(1)/sqrt(2) xx (1)/sqrt(2) + (1)/sqrt(2)`
⇒ tan x = `(1)/(2) + (1)/(2)`
⇒ tan x = 1
⇒ tan x = tan 45°
⇒ x = 45°.
APPEARS IN
संबंधित प्रश्न
Evaluate the following expression:
(i) `tan 60º cosec^2 45º + sec^2 60º tan 45º`
(ii) `4cot^2 45º – sec^2 60º + sin^2 60º + cos^2 90º.`
Evaluate the following:
2tan2 45° + cos2 30° − sin2 60°
Show that tan 48° tan 23° tan 42° tan 67° = 1
Evaluate the following :
`((sin 49^@)/(cos 41^@))^2 + (cos 41^@/(sin 49^@))^2`
Evaluate the following :
sin 35° sin 55° − cos 35° cos 55°
If A, B, C are the interior angles of a triangle ABC, prove that
`tan ((C+A)/2) = cot B/2`
Prove that `cos 80^@/sin 10^@ + cos 59^@ cosec 31^@ = 2`
Without using trigonometric tables, prove that:
cos54° cos36° − sin54° sin36° = 0
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°
If cos 20 = sin 4 θ ,where 2 θ and 4 θ are acute angles, then find the value of θ
prove that:
sin (2 × 30°) = `(2 tan 30°)/(1+tan^2 30°)`
find the value of: tan 30° tan 60°
Prove that:
3 cosec2 60° - 2 cot2 30° + sec2 45° = 0
Prove that:
4 (sin4 30° + cos4 60°) -3 (cos2 45° - sin2 90°) = 2
If sin x = cos y; write the relation between x and y, if both the angles x and y are acute.
If A = B = 45° ,
show that:
cos (A + B) = cos A cos B - sin A sin B
If A = 30°;
show that:
cos 2A = cos4 A - sin4 A
Without using tables, evaluate the following: sin230° cos245° + 4tan230° + sin290° + cos20°
Without using tables, evaluate the following: cosec330° cos60° tan345° sin290° sec245° cot30°.
Prove that: sin60°. cos30° - sin60°. sin30° = `(1)/(2)`
Find the value of x in the following: `sqrt(3)`tan 2x = cos60° + sin45° cos45°
Find the value of x in the following: cos2x = cos60° cos30° + sin60° sin30°
Without using table, find the value of the following: `(tan^2 60° + 4cos^2 45° + 3sec^2 30° + 5cos90°)/(cosec30° + sec60° - cot^2 30°)`
If tan `"A" = (1)/(2), tan "B" = (1)/(3) and tan("A" + "B") = (tan"A" + tan"B")/(1 - tan"A" tan"B")`, find A + B.
Verify the following equalities:
sin2 60° + cos2 60° = 1
Find the value of the following:
sin2 30° – 2 cos3 60° + 3 tan4 45°
Find the value of 8 sin 2x, cos 4x, sin 6x, when x = 15°
If 2 sin 2θ = `sqrt(3)` then the value of θ is
If A and B are acute angles such that sin (A – B) = 0 and 2 cos (A + B) – 1 = 0, then find angles A and B.