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प्रश्न
\[\frac{x^2 - 1}{2x}\] is equal to
विकल्प
sec θ + tan θ
sec θ − tan θ
sec2 θ + tan2 θ
sec2 θ − tan2 θ
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उत्तर
The given expression is `sqrt ((1+sinθ)/(1-sinθ))`
Multiplying both the numerator and denominator under the root by `1+ sinθ`, we have
`sqrt (((1+ sinθ)(1+sin θ))/((1+sin θ)(1-sinθ)))`
`=sqrt((1+sinθ)/((1- sin^2θ)))`
`= sqrt((1+ sinθ)^2/cos^2θ)`
=`(1+sinθ)/cosθ`
=` 1/cosθ+sinθ/cosθ`
=` sec θ+tan θ`
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संबंधित प्रश्न
If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`
Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`
As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.
Prove the following trigonometric identity.
`cos^2 A + 1/(1 + cot^2 A) = 1`
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`
`If sin theta = cos( theta - 45° ),where theta " is acute, find the value of "theta` .
If tanθ `= 3/4` then find the value of secθ.
If x = a sec θ and y = b tan θ, then b2x2 − a2y2 =
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`(1 + cotA + tanA)(sinA - cosA) = secA/(cosec^2A) - (cosecA)/sec^2A`
Evaluate:
`(tan 65°)/(cot 25°)`
Without using the trigonometric table, prove that
tan 10° tan 15° tan 75° tan 80° = 1
Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.
Activity:
L.H.S. = `square`
= `cos^2θ xx square` ...`[1 + tan^2θ = square]`
= `(cos θ xx square)^2`
= 12
= 1
= R.H.S.
Prove that `(1 + sin θ)/(1 - sin θ) = (sec θ + tan θ)^2`.
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The value of 2sinθ can be `a + 1/a`, where a is a positive number, and a ≠ 1.
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
If 2sin2θ – cos2θ = 2, then find the value of θ.
If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p2 – 1) = 2p.
