Advertisements
Advertisements
Question
Evaluate: `4(sin^2 30 + cos^4 60^@) - 2/3 3[(sqrt(3/2))^2 . [1/sqrt2]^2] + 1/4 (sqrt3)^2`
Solution
`sin 30^@ = 1/2, cos 60 = 1/2, sin 60^@ = sqrt3/2, cos 45^@ = 1/sqrt2, tan 60^@ = sqrt3`
`=> 4[[1/2]^4 + [1/2]^4] - 2/3[(sqrt3/2)^2 - (1/sqrt2)^2] + 1/2 (sqrt3)^2`
`4[2. 1/16] - 2/3 [3/4 - 1/2] + 3/2`
`= 1/2 - 2/3 . 1/4 + 3/2 = 11/6`
APPEARS IN
RELATED QUESTIONS
Evaluate the following in the simplest form:
sin 60° cos 30° + cos 60° sin 30°
`(2 tan 30°)/(1+tan^2 30°)` = ______.
Evaluate the following:
`(sin 20^@)/(cos 70^@)`
If A, B, C are the interior angles of a triangle ABC, prove that
`tan ((C+A)/2) = cot B/2`
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:
cos 30° . cos 60° - sin 30° . sin 60° = 0
If A = 30°;
show that:
(sinA - cosA)2 = 1 - sin2A
Without using tables, evaluate the following: cosec330° cos60° tan345° sin290° sec245° cot30°.
Verify the following equalities:
1 + tan2 30° = sec2 30°
