Advertisements
Advertisements
Question
Find the value of:
tan2 30° + tan2 45° + tan2 60°
Solution
tan2 30° + tan2 45° + tan2 60° = `(1/sqrt3)^2 + 1^2 + (sqrt3)^2`
= `(1)/(3) + 1+ 3`
= `(13)/(3)`
= `4(1)/(3)`
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.`
Using the formula, sin(A – B) = sinA cosB – cosA sinB, find the value of sin 15º
State whether the following is true or false. Justify your answer.
sinθ = cosθ for all values of θ.
Evaluate the following :
`(sin 21^@)/(cos 69^@)`
Evaluate the following :
`(cot 40^@)/cos 35^@ - 1/2 [(cos 35^@)/(sin 55^@)]`
Evaluate the following :
(sin 72° + cos 18°) (sin 72° − cos 18°)
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
cosec 54° + sin 72°
If Sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A =?
Prove the following :
`(cos(90^@ - theta) sec(90^@ - theta)tan theta)/(cosec(90^@ - theta) sin(90^@ - theta) cot (90^@ - theta)) + tan (90^@ - theta)/cot theta = 2`
Prove the following :
`(cos(90°−A) sin(90°−A))/tan(90°−A) - sin^2 A = 0`
Evaluate: `(3 cos 55^@)/(7 sin 35^@) - (4(cos 70 cosec 20^@))/(7(tan 5^@ tan 25^@ tan 45^@ tan 65^@ tan 85^@))`
Evaluate: `cos 58^@/sin 32^@ + sin 22^@/cos 68^@ - (cos 38^@ cosec 52^@)/(tan 18^@ tan 35^@ tan 60^@ tan 72^@ tan 65^@)`
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratios: sin 45°
Evaluate:
`(cos3"A" – 2cos4"A")/(sin3"A" + 2sin4"A")` , when A = 15°
Given A = 60° and B = 30°,
prove that : sin (A + B) = sin A cos B + cos A sin B
If tan (A + B) = 1 and tan(A-B)`=1/sqrt3` , 0° < A + B < 90°, A > B, then find the values of A and B.
Prove that:
cosec2 45° - cot2 45° = 1
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratio: cos 45°
If tan θ = cot θ and 0°∠θ ∠90°, state the value of θ
secθ . Cot θ= cosecθ ; write true or false
Evaluate :
`(3 sin 3"B" + 2 cos(2"B" + 5°))/(2 cos 3"B" – sin (2"B" – 10°)` ; when "B" = 20°.
If A =30o, then prove that :
sin 3A = 3 sin A - 4 sin3A.
Without using tables, evaluate the following: tan230° + tan260° + tan245°
Without using tables, evaluate the following: 4(sin430° + cos460°) - 3(cos245° - sin290°).
Without using tables, find the value of the following: `(sin30°)/(sin45°) + (tan45°)/(sec60°) - (sin60°)/(cot45°) - (cos30°)/(sin90°)`
Prove that: sin60°. cos30° - sin60°. sin30° = `(1)/(2)`
Find the value of x in the following: 2 sin3x = `sqrt(3)`
Find the value of the following:
`(tan45^circ)/("cosec"30^circ) + (sec60^circ)/(cot45^circ) - (5sin90^circ)/(2cos0^circ)`
If 2 sin 2θ = `sqrt(3)` then the value of θ is
