Advertisements
Advertisements
Question
Prove that:
cos 30° . cos 60° - sin 30° . sin 60° = 0
Solution
LHS=cos 30°. cos 60° - sin 30°. sin 60°
= `(sqrt3)/(2) (1)/(2) – (1)/(2) (sqrt3)/(2) = (sqrt3)/(4) – (sqrt3)/(4) = 0 = RHS`
APPEARS IN
RELATED QUESTIONS
Find the value of x in the following :
tan 3x = sin 45º cos 45º + sin 30º
Evaluate the following in the simplest form: sin 60º cos 45º + cos 60º sin 45º
Evaluate the following:
`(cos 45°)/(sec 30° + cosec 30°)`
`(1- tan^2 45°)/(1+tan^2 45°)` = ______
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
sec 50º sin 40° + cos 40º cosec 50º
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
cosec 54° + sin 72°
Prove that tan 20° tan 35° tan 45° tan 55° tan 70° = 1
Prove the following
sin θ sin (90° − θ) − cos θ cos (90° − θ) = 0
Evaluate: Cosec (65 + θ) – sec (25 – θ) – tan (55 – θ) + cot (35 + θ)
Evaluate: tan 7° tan 23° tan 60° tan 67° tan 83°
Evaluate: `sin 18^@/cos 72^@ + sqrt3 [tan 10° tan 30° tan 40° tan 50° tan 80°]`
Prove that
tan (55° − θ) − cot (35° + θ) = 0
Prove that
cosec (67° + θ) − sec (23° − θ) = 0
Find the value of:
tan2 30° + tan2 45° + tan2 60°
Given A = 60° and B = 30°,
prove that : sin (A + B) = sin A cos B + cos A sin B
If A =30o, then prove that :
sin 2A = 2sin A cos A = `(2 tan"A")/(1 + tan^2"A")`
find the value of: cosec2 60° - tan2 30°
For any angle θ, state the value of: sin2 θ + cos2 θ
Without using table, find the value of the following:
`(sin30° - sin90° + 2cos0°)/(tan30° tan60°)`
Without using tables, find the value of the following: `(tan45°)/("cosec"30°) + (sec60°)/(cot45°) - (5sin90°)/(2cos0°)`
If A = 30° and B = 60°, verify that: sin (A + B) = sin A cos B + cos A sin B
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.
The value of `(2tan30^circ)/(1 - tan^2 30^circ)` is equal to
The value of `(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` is
The value of cos1°. cos2°. cos3°. cos4°....................... cos90° is ______.
Find the value of x if `2 "cosec"^2 30 + x sin^2 60 - 3/4 tan^2 30` = 10
Evaluate: sin2 60° + 2tan 45° – cos2 30°.
