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प्रश्न
cos 45° = ?
विकल्प
sin 45°
sec 45°
cot 45°
tan 45°
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उत्तर
sin 45°
Explanation:
`cos 45^circ = 1/sqrt2`, `sin 45^circ = 1/sqrt(2)`
∴ cos 45° = sin 45°
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संबंधित प्रश्न
Prove the following trigonometric identities
`cos theta/(1 - sin theta) = (1 + sin theta)/cos theta`
Prove the following identities:
(sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = sec A + tan A`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
`(sectheta- tan theta)/(sec theta + tan theta) = ( cos ^2 theta)/( (1+ sin theta)^2)`
If (tan θ + sin θ) = m and (tan θ – sin θ) = n, prove that (m2 – n2)2 = 16 mn.
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
If `cos theta = 7/25 , "write the value of" ( tan theta + cot theta).`
If `sqrt(3) sin theta = cos theta and theta ` is an acute angle, find the value of θ .
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
For ΔABC , prove that :
`tan ((B + C)/2) = cot "A/2`
Evaluate:
`(tan 65°)/(cot 25°)`
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
Prove that `(sin θ + tan θ)/(cos θ) = tan θ (1 + sec θ)`.
Show that, cotθ + tanθ = cosecθ × secθ
Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
