Advertisements
Advertisements
प्रश्न
`sqrt((1 - cos^2theta) sec^2 theta) = tan theta`
विकल्प
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
`sqrt((1 - cos^2 theta) sec^2 theta)`
= `sqrt(sin^2 theta * sec^2 theta)` ...[∵ sin2θ + cos2θ = 1]
= `sqrt(sin^2 theta * 1/(cos^2 theta)` ...`[∵ sec theta = 1/costheta, tan theta = sin theta/cos theta]`
= `sqrt(tan^2 theta)`
= tan θ
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Prove the following trigonometric identities.
`(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`
Prove the following identities:
cot2 A – cos2 A = cos2 A . cot2 A
Prove the following identities:
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
`cos^2 theta + 1/((1+ cot^2 theta )) =1`
`(cot ^theta)/((cosec theta+1)) + ((cosec theta + 1))/cot theta = 2 sec theta`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)
Prove that sec2 (90° - θ) + tan2 (90° - θ) = 1 + 2 cot2 θ.
Without using a trigonometric table, prove that
`(cos 70°)/(sin 20°) + (cos 59°)/(sin 31°) - 8sin^2 30° = 0`.
Prove the following identities:
`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ
The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.
If 2sin2θ – cos2θ = 2, then find the value of θ.
Show that `(cos^2(45^circ + θ) + cos^2(45^circ - θ))/(tan(60^circ + θ) tan(30^circ - θ)) = 1`
