Advertisements
Advertisements
प्रश्न
Without using tables, evaluate the following: tan230° + tan260° + tan245°
उत्तर
tan230° + tan260° + tan245°
tan30° = `(1)/sqrt(3)`
tan60° = `sqrt(3)`
tan45° = 1
tan230° + tan260° + tan245°
= `(1/sqrt(3))^2 + (sqrt(3))^2 + 1`
= `(1)/(3) + 3 + 1`
= `(1 + 9 + 3)/(3)`
= `(13)/(3)`.
APPEARS IN
संबंधित प्रश्न
If A, B and C are interior angles of a triangle ABC, then show that `\sin( \frac{B+C}{2} )=\cos \frac{A}{2}`
Find the value of x in the following :
tan 3x = sin 45º cos 45º + sin 30º
If x = 30°, verify that
(i) `\tan 2x=\frac{2\tan x}{1-\tan ^{2}x`
(ii) `\sin x=\sqrt{\frac{1-\cos 2x}{2}}`
An equilateral triangle is inscribed in a circle of radius 6 cm. Find its side.
Evaluate the following in the simplest form: sin 60º cos 45º + cos 60º sin 45º
Evaluate cos 48° − sin 42°
Evaluate the following :
`tan 35^@/cot 55^@ + cot 78^@/tan 12^@ -1`
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°
cos 78° + sec 78°
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
Prove the following :
`(cos(90°−A) sin(90°−A))/tan(90°−A) - sin^2 A = 0`
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 :
3sin2 30° + 2tan2 60° - 5cos2 45°
prove that:
cos (2 x 30°) = `(1 – tan^2 30°)/(1+tan^2 30°)`
If A = 30°;
show that:
`(1 – cos 2"A")/(sin 2"A") = tan"A"`
If A = 30°;
show that:
`(cos^3"A" – cos 3"A")/(cos "A") + (sin^3"A" + sin3"A")/(sin"A") = 3`
Without using tables, evaluate the following: sin230° cos245° + 4tan230° + sin290° + cos20°
Find the value of x in the following: tan x = sin45° cos45° + sin30°
If A = 30° and B = 60°, verify that: `(sin("A" + "B"))/(cos"A" . cos"B")` = tanA + tanB
In ΔABC right angled at B, ∠A = ∠C. Find the value of:
(i) sinA cosC + cosA sinC
(ii) sinA sinB + cosA cosB
Verify the following equalities:
sin 30° cos 60° + cos 30° sin 60° = sin 90°
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
Evaluate: `(5 "cosec"^2 30^circ - cos 90^circ)/(4 tan^2 60^circ)`
Evaluate: `(5cos^2 60° + 4sec^2 30° - tan^2 45°)/(sin^2 30° + sin^2 60°)`
