Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities
`((1 + sin theta)^2 + (1 + sin theta)^2)/(2cos^2 theta) = (1 + sin^2 theta)/(1 - sin^2 theta)`
Advertisements
उत्तर
LHS = `(1 sin^2 theta + 2 sin theta + 1 + sin^2 theta - 2 sin theta)/(2 cos theta)`
`=> (2(1 + sin^2 theta))/(2 cos^2 theta) => (1 + sin^2 theta)/(1 - sin^2 theta)` `[∵ cos^2 theta = 1 - sin^2 theta]`
∴ LHS = RHS Hence proved
APPEARS IN
संबंधित प्रश्न
Prove that: `(1 – sinθ + cosθ)^2 = 2(1 + cosθ)(1 – sinθ)`
Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
Write the value of `(cot^2 theta - 1/(sin^2 theta))`.
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
Simplify : 2 sin30 + 3 tan45.
If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ?
(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to
Prove the following identity :
`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`
Find the value of sin 30° + cos 60°.
Find A if tan 2A = cot (A-24°).
If 5x = sec θ and `5/x` = tan θ, then `x^2 - 1/x^2` is equal to
Prove that `(1 + sec "A")/"sec A" = (sin^2"A")/(1 - cos"A")`
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.
Prove the following trigonometry identity:
(sin θ + cos θ)(cosec θ – sec θ) = cosec θ ⋅ sec θ – 2 tan θ
