Advertisements
Advertisements
Question
Prove that:
cos2 30° - sin2 30° = cos 60°
Solution
`(sqrt3/2)^2 - (1/2)^2 = 3/4 - 1/4 = 2/4 = 1/2 = cos60°`
APPEARS IN
RELATED QUESTIONS
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.`
Show that:
(i) `2(cos^2 45º + tan^2 60º) – 6(sin^2 45º – tan^2 30º) = 6`
(ii) `2(cos^4 60º + sin^4 30º) – (tan^2 60º + cot^2 45º) + 3 sec^2 30º = 1/4`
Find the value of x in the following :
tan 3x = sin 45º cos 45º + sin 30º
`(1- tan^2 45°)/(1+tan^2 45°)` = ______
State whether the following are true or false. Justify your answer.
cot A is not defined for A = 0°.
Evaluate cos 48° − sin 42°
Evaluate the following :
`((sin 27^@)/(cos 63^@))^2 - (cos 63^@/sin 27^@)^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°
Sin 59° + cos 56°
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
cosec 54° + sin 72°
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
cot 85° + cos 75°
Evaluate tan 35° tan 40° tan 50° tan 55°
Evaluate: `cos 58^@/sin 32^@ + sin 22^@/cos 68^@ - (cos 38^@ cosec 52^@)/(tan 18^@ tan 35^@ tan 60^@ tan 72^@ tan 65^@)`
Without using trigonometric tables, prove that:
cos54° cos36° − sin54° sin36° = 0
find the value of: sin2 30° + cos2 30°+ cot2 45°
Prove that:
cos 30° . cos 60° - sin 30° . sin 60° = 0
If sec A = cosec A and 0° ∠A ∠90°, state the value of A
If A = 30°;
show that:
(sinA - cosA)2 = 1 - sin2A
If A = 30°;
show that:
`(1 – cos 2"A")/(sin 2"A") = tan"A"`
If A = 30°;
show that:
4 cos A cos (60° - A). cos (60° + A) = cos 3A
Without using tables, evaluate the following sec45° sin45° - sin30° sec60°.
Without using tables, evaluate the following: 4(sin430° + cos460°) - 3(cos245° - sin290°).
Prove that: `((cot30° + 1)/(cot30° -1))^2 = (sec30° + 1)/(sec30° - 1)`
Find the value of x in the following: 2 sin3x = `sqrt(3)`
If sinθ = cosθ and 0° < θ<90°, find the value of 'θ'.
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 sin(A +B) = 1(A -B) = 1, find A and B.
Verify the following equalities:
sin 30° cos 60° + cos 30° sin 60° = sin 90°
If sin 30° = x and cos 60° = y, then x2 + y2 is
Evaluate: sin2 60° + 2tan 45° – cos2 30°.
