Advertisements
Advertisements
प्रश्न
prove that:
sin (2 × 30°) = `(2 tan 30°)/(1+tan^2 30°)`
उत्तर
RHS = `(2 tan 30°)/(1+tan^2 30°) = (2xx1/(sqrt3))/(1 +(1/sqrt3)^2) = (2/(sqrt3))/(1+(1)/(3)) = (2/sqrt3)/(4/(3)) =2/sqrt3xx3/4=3/(2sqrt3)xxsqrt3/sqrt3=(3sqrt3)/(2xx3)= (sqrt3)/(2)`
LHS = sin (2 × 30°) = sin 60° = `(sqrt3)/(2)`
∴ LHS = RHS
APPEARS IN
संबंधित प्रश्न
Evaluate the following in the simplest form:
sin 60° cos 30° + cos 60° sin 30°
Evaluate the following:
`(5cos^2 60° + 4sec^2 30° - tan^2 45°)/(sin^2 30° + cos^2 30°)`
`(2 tan 30°)/(1+tan^2 30°)` = ______.
State whether the following is true or false. Justify your answer.
The value of cos θ increases as θ increases.
Evaluate the following :
`((sin 49^@)/(cos 41^@))^2 + (cos 41^@/(sin 49^@))^2`
Evaluate the following :
`(cot 40^@)/cos 35^@ - 1/2 [(cos 35^@)/(sin 55^@)]`
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`
Prove that:
sin 60° = 2 sin 30° cos 30°
If sin x = cos x and x is acute, state the value of x
find the value of: cos2 60° + sec2 30° + tan2 45°
If `sqrt3` = 1.732, find (correct to two decimal place) the value of `(2)/(tan 30°)`
Evaluate :
`(3 sin 3"B" + 2 cos(2"B" + 5°))/(2 cos 3"B" – sin (2"B" – 10°)` ; when "B" = 20°.
Given A = 60° and B = 30°,
prove that : cos (A + B) = cos A cos B - sin A sin B
Given A = 60° and B = 30°,
prove that : cos (A - B) = cos A cos B + sin A sin B
Given A = 60° and B = 30°,
prove that: tan (A - B) = `(tan"A" – tan"B")/(1 + tan"A".tan"B")`
If A = 30°;
show that:
cos 2A = cos4 A - sin4 A
If A = 30°;
show that:
`(1 – cos 2"A")/(sin 2"A") = tan"A"`
Without using tables, evaluate the following: sin230° sin245° + sin260° sin290°.
Without using tables, evaluate the following: tan230° + tan260° + tan245°
Prove that: sin60°. cos30° - sin60°. sin30° = `(1)/(2)`
If A = 30° and B = 60°, verify that: sin (A + B) = sin A cos B + cos A sin B
If A = 30° and B = 60°, verify that: `(sin("A" + "B"))/(cos"A" . cos"B")` = tanA + tanB
If A = B = 45°, verify that sin (A - B) = sin A .cos B - cos A.sin B
If A = B = 45°, verify that cos (A − B) = cos A. cos B + sin A. sin B
If sin(A - B) = sinA cosB - cosA sinB and cos(A - B) = cosA cosB + sinA sinB, find the values of sin15° and cos15°.
If sin(A +B) = 1(A -B) = 1, find A and B.
