Advertisements
Advertisements
प्रश्न
Prove that: sin60°. cos30° - sin60°. sin30° = `(1)/(2)`
उत्तर
L.H.S. = sin60° . cos30° - cos60° . sin30°
= `sqrt(3)/(2) xx sqrt(3)/(2) - (1)/(2) xx (1)/(2)`
= `(3)/(4) - (1)/(4)`
= `(2)/(4)`
= `(1)/(2)`
= R.H.S.
APPEARS IN
संबंधित प्रश्न
If A, B and C are interior angles of a triangle ABC, then show that `\sin( \frac{B+C}{2} )=\cos \frac{A}{2}`
Find the value of x in the following :
tan 3x = sin 45º cos 45º + sin 30º
State whether the following is true or false. Justify your answer.
The value of sinθ increases as θ increases.
Evaluate the following:
`(sin 20^@)/(cos 70^@)`
Evaluate the following :
`cos 19^@/sin 71^@`
Evaluate the following :
`((sin 49^@)/(cos 41^@))^2 + (cos 41^@/(sin 49^@))^2`
If Sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A =?
Prove that sin 48° sec 42° + cos 48° cosec 42° = 2
Prove the following
sin (50° − θ) − cos (40° − θ) + tan 1° tan 10° tan 20° tan 70° tan 80° tan 89° = 1
Evaluate:
`2/3 (cos^4 30° - sin^4 45°) - 3(sin^2 60° - sec^2 45°) + 1/4 cot^2 30°`.
Evaluate: `(2sin 68)/cos 22 - (2 cot 15^@)/(5 tan 75^@) - (8 tan 45^@ tan 20^@ tan 40^@ tan 50^@ tan 70^@)/5`
Evaluate: `(3 cos 55^@)/(7 sin 35^@) - (4(cos 70 cosec 20^@))/(7(tan 5^@ tan 25^@ tan 45^@ tan 65^@ tan 85^@))`
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
sec78° + cosec56°
prove that:
sin (2 × 30°) = `(2 tan 30°)/(1+tan^2 30°)`
find the value of: cosec2 60° - tan2 30°
find the value of :
`( tan 45°)/ (cos ec30°) +( sec60°)/(co 45°) – (5 sin 90°)/ (2 cos 0°)`
prove that:
cos (2 x 30°) = `(1 – tan^2 30°)/(1+tan^2 30°)`
prove that:
tan (2 x 30°) = `(2 tan 30°)/(1– tan^2 30°)`
If sin x = cos y; write the relation between x and y, if both the angles x and y are acute.
If A = 30°;
show that:
`(1 – cos 2"A")/(sin 2"A") = tan"A"`
Without using tables, evaluate the following: (sin90° + sin45° + sin30°)(sin90° - cos45° + cos60°).
Without using tables, find the value of the following: `(4)/(cot^2 30°) + (1)/(sin^2 60°) - cos^2 45°`
Prove that : sec245° - tan245° = 1
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 sinθ = cosθ and 0° < θ<90°, find the value of 'θ'.
Verify the following equalities:
sin 30° cos 60° + cos 30° sin 60° = sin 90°
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.
The value of 5 sin2 90° – 2 cos2 0° is ______.
Evaluate: sin2 60° + 2tan 45° – cos2 30°.
