Advertisements
Advertisements
Question
If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.
Solution
LHS = sin 2A
Putting A = 30° in LHS and RHS., we get
LHS = sin 2 x 30° = sin 60° = `sqrt3/2`
RHS = `(2 xx tan 30°)/(1 + tan^2 30°) = (2 xx 1/sqrt3)/( 1 + (1/sqrt3)^2)`
= `(2/sqrt3)/(1 + 1/3). (2/sqrt3)/(4/3)`
= `(2 xx 3)/(sqrt3 xx 4) = sqrt3/4`
Hence,
LHS = RHS
Hence proved.
APPEARS IN
RELATED QUESTIONS
If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p2 – 1) = 2p
Evaluate without using trigonometric tables:
`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`
Prove the following trigonometric identities.
`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`
Prove the following identities:
(1 – tan A)2 + (1 + tan A)2 = 2 sec2A
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`
`(sec theta + tan theta )/( sec theta - tan theta ) = ( sec theta + tan theta )^2 = 1+2 tan^2 theta + 25 sec theta tan theta `
If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`
If 5x = sec ` theta and 5/x = tan theta , " find the value of 5 "( x^2 - 1/( x^2))`
Prove that: 2(sin6θ + cos6θ) - 3 ( sin4θ + cos4θ) + 1 = 0.
