Advertisements
Advertisements
प्रश्न
If \[\frac{{cosec}^2 \theta - \sec^2 \theta}{{cosec}^2 \theta + \sec^2 \theta}\] write the value of \[\frac{1 - \cos^2 \theta}{2 - \sin^2 \theta}\]
उत्तर
Given: `cot θ=1/sqrt3`
`"Base"/"Perpendicular"=1/sqrt3`
`"Base"=1`
`"Perpendicular"=sqrt3`
`"Hypotenuse"= sqrt(("Perpendicular")^2+(Base)^2)`
`"Hypotenuse"=2`
Now we find, `(1-cos^2 θ)/(2- sin^2 θ)`
= `(1- ("Base")^2/("hypotenuse")^2)/ (2-("Perpendicular")^2/("hypotenuse")^2)`
=`(1-(1)^2/(2)^2)/(2-(sqrt3)^2/(2)^2)`
=`(1-1/4)/(2-3/4)`
=`3/5`
Hence the value of `(1-cos^2θ)/(2-sin^2θ)` is `3/5`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
(secθ + cosθ) (secθ − cosθ) = tan2θ + sin2θ
For triangle ABC, show that : `sin (A + B)/2 = cos C/2`
A triangle ABC is right angles at B; find the value of`(secA.cosecC - tanA.cotC)/sinB`
Find the value of angle A, where 0° ≤ A ≤ 90°.
sin (90° – 3A) . cosec 42° = 1
Use tables to find the acute angle θ, if the value of tan θ is 0.4741
Evaluate:
`sec26^@ sin64^@ + (cosec33^@)/sec57^@`
Evaluate:
sin 27° sin 63° – cos 63° cos 27°
Find A, if 0° ≤ A ≤ 90° and cos2 A – cos A = 0
If 0° < A < 90°; find A, if `sinA/(secA - 1) + sinA/(secA + 1) = 2`
If \[\tan A = \frac{3}{4} \text{ and } A + B = 90°\] then what is the value of cot B?
Write the value of tan 10° tan 15° tan 75° tan 80°?
If \[\frac{160}{3}\] \[\tan \theta = \frac{a}{b}, \text{ then } \frac{a \sin \theta + b \cos \theta}{a \sin \theta - b \cos \theta}\]
If θ is an acute angle such that \[\tan^2 \theta = \frac{8}{7}\] then the value of \[\frac{\left( 1 + \sin \theta \right) \left( 1 - \sin \theta \right)}{\left( 1 + \cos \theta \right) \left( 1 - \cos \theta \right)}\]
If angles A, B, C to a ∆ABC from an increasing AP, then sin B =
The value of cos 1° cos 2° cos 3° ..... cos 180° is
If sin θ =7/25, where θ is an acute angle, find the value of cos θ.
Find the sine ratio of θ in standard position whose terminal arm passes through (4,3)
Find the value of the following:
tan 15° tan 30° tan 45° tan 60° tan 75°
If sin θ + sin² θ = 1 then cos² θ + cos4 θ is equal ______.
The value of (tan1° tan2° tan3° ... tan89°) is ______.
