Advertisements
Advertisements
Question
Evaluate the following
tan2 30° + tan2 60° + tan2 45°
Advertisements
Solution
tan2 30° + tan2 60° + tan2 45° ....(i)
By trigonometric ratios we have
`tan 30^@ = 1/sqrt3 tan 60^@ = sqrt3 tan 45^@ = 1`
By substituting above values in (i), we get
`[1/sqrt3]^2 + [sqrt3]^2 + [1]^2`
`=> 1/3 + 3 + 1 => 1/3 + 4`
`=> (1 + 12)/3 = 13/3`
RELATED QUESTIONS
State whether the following are true or false. Justify your answer.
The value of tan A is always less than 1.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sec theta = 13/5`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cos theta = 12/2`
if `cos theta = 3/5`, find the value of `(sin theta - 1/(tan theta))/(2 tan theta)`
If `tan θ = 20/21` show that `(1 - sin theta + cos theta)/(1 + sin theta + cos theta) = 3/7`
Evaluate the following
cos 60° cos 45° - sin 60° ∙ sin 45°
Evaluate the following:
(cosec2 45° sec2 30°)(sin2 30° + 4 cot2 45° − sec2 60°)
Evaluate the Following
(cos 0° + sin 45° + sin 30°)(sin 90° − cos 45° + cos 60°)
Evaluate the Following:
`tan 45^@/(cosec 30^@) + sec 60^@/cot 45^@ - (5 sin 90^@)/(2 cos 0^@)`
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.
The value of cos 0°. cos 1°. cos 2°. cos 3°… cos 89° cos 90° is ______.
If cos A = `4/5`, then the value of tan A is ______.
In ΔABC, ∠ABC = 90° and ∠ACB = θ. Then write the ratios of sin θ and tan θ from the figure.
Find the value of sin 45° + cos 45° + tan 45°.
Prove that: cot θ + tan θ = cosec θ·sec θ
Proof: L.H.S. = cot θ + tan θ
= `square/square + square/square` ......`[∵ cot θ = square/square, tan θ = square/square]`
= `(square + square)/(square xx square)` .....`[∵ square + square = 1]`
= `1/(square xx square)`
= `1/square xx 1/square`
= cosec θ·sec θ ......`[∵ "cosec" θ = 1/square, sec θ = 1/square]`
= R.H.S.
∴ L.H.S. = R.H.S.
∴ cot θ + tan θ = cosec·sec θ
If cos(α + β) = `(3/5)`, sin(α – β) = `5/13` and 0 < α, β < `π/4`, then tan (2α) is equal to ______.
If f(x) = `3cos(x + (5π)/6) - 5sinx + 2`, then maximum value of f(x) is ______.
If sin θ – cos θ = 0, then find the value of sin4 θ + cos4 θ.
