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प्रश्न
If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.
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उत्तर
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.
संबंधित प्रश्न
Prove the following trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
Prove the following identities:
`1/(1 - sinA) + 1/(1 + sinA) = 2sec^2A`
`1/((1+ sin θ)) + 1/((1 - sin θ)) = 2 sec^2 θ`
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove the following identity :
`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
If `sec θ + tan θ = sqrt(3)`, complete the activity to find the value of sec θ – tan θ.
Activity:
`square = 1 + tan^2θ` ...[Fundamental trigonometric identity]
`square - tan^2θ = 1`
`(sec θ + tan θ) . (sec θ - tan θ) = square`
`sqrt(3) . (sec θ - tan θ) = 1`
`(sec θ - tan θ) = square`
If `sec θ = 41/40`, then find values of sin θ, cot θ, cosec θ.
Show that `(cos^2(45^circ + θ) + cos^2(45^circ - θ))/(tan(60^circ + θ) tan(30^circ - θ)) = 1`
