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प्रश्न
` (sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta) = 2/ ((1- 2 cos^2 theta))`
उत्तर
LHS = `(sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta)`
=` ((sin theta + cos theta )^2 + ( sin theta - cos theta)^2)/(( sin theta - cos theta ) ( sin theta + cos theta))`
=`( sin^2 theta + cos^2 theta + 2 sin theta cos theta + sin^2 theta + cos^2 theta - 2 sin theta cos theta)/((sin^2 theta - cos^2 theta))`
=`(1+1)/((- cos^ 2theta )- cos^2 theta) (∵ sin^ 2theta + cos^2 theta =1)`
=`2/(1-2 cos^2 theta)`
= RHS
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संबंधित प्रश्न
Prove the following trigonometric identities:
`(1 - cos^2 A) cosec^2 A = 1`
Prove the following trigonometric identities.
`(1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta`
Prove the following identities:
`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
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`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`
Prove that:
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
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`(cosecθ)/(tanθ + cotθ) = cosθ`
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Prove that `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ)) = 1/(tan θ + cot θ)`
Prove that identity:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
If x = a tan θ and y = b sec θ then
If 3 sin θ = 4 cos θ, then sec θ = ?
Find the value of sin2θ + cos2θ
Solution:
In Δ ABC, ∠ABC = 90°, ∠C = θ°
AB2 + BC2 = `square` .....(Pythagoras theorem)
Divide both sides by AC2
`"AB"^2/"AC"^2 + "BC"^2/"AC"^2 = "AC"^2/"AC"^2`
∴ `("AB"^2/"AC"^2) + ("BC"^2/"AC"^2) = 1`
But `"AB"/"AC" = square and "BC"/"AC" = square`
∴ `sin^2 theta + cos^2 theta = square`
