Advertisements
Advertisements
प्रश्न
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove the following:
(sin A + cos A)2 + (cos A – sin A)2 = 2
Advertisements
उत्तर
L.H.S. = (cos A + sin A)2 + (cos A – sin A)2
= cos2 A + sin2 A + 2 cos A . sin A + cos2 A + sin2 A – 2 cos A . sin A
= 2 sin2 A + 2 cos2 A
= 2(sin2 A + cos2 A) ...(∵ sin2 A + cos2 A = 1)
= 2 × 1
= 2
= R.H.S.
संबंधित प्रश्न
Prove the following trigonometric identity:
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
Prove the following trigonometric identities.
`((1 + sin theta - cos theta)/(1 + sin theta + cos theta))^2 = (1 - cos theta)/(1 + cos theta)`
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
Prove the following identities:
`(1+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`
If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
