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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
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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 identities:
(i) (1 – sin2θ) sec2θ = 1
(ii) cos2θ (1 + tan2θ) = 1
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
If sec θ = `25/7`, then find the value of tan θ.
If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.
If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.
Prove that `(cos(90^circ - A))/(sin A) = (sin(90^circ - A))/(cos A)`.
sin4A – cos4A = 1 – 2cos2A. For proof of this complete the activity given below.
Activity:
L.H.S. = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` ...`[sin^2"A" + square = 1]`
= `square` – cos2A ...[sin2A = 1 – cos2A]
= `square`
= R.H.S.
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
