Advertisements
Advertisements
प्रश्न
Prove that `(sec8 theta - 1)/(sec4 theta - 1) = (tan8 theta)/(tan2 theta)`
Advertisements
उत्तर
We have `(sec8 theta - 1)/(sec4 theta - 1) = ((1 - cos8 theta) cos 4theta)/(cos 8theta(1 - cos4theta))`
= `(2sin^2 4theta cos 4theta)/(cos8theta 2sin^2 2theta)`
= `(sin4theta(2sin4theta cos 4theta))/(2cos8theta sin^2 2theta)`
= `(sin4theta sin 8theta)/(2 cos8 theta sin^2 2theta)`
= `(2sin 2theta cos 2theta sin 8theta)/(2 cos8theta sin^2 2theta)`
= `(tan8 theta)/(tan 2theta)`
APPEARS IN
संबंधित प्रश्न
Find the radian measure corresponding to the following degree measure:
25°
Find the degree measure corresponding to the following radian measure `(use pi = 22/7)`
`11/16`
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm
(Use `pi = 22/7`)
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
10 cm
Find the degree measure corresponding to the following radian measure:
\[\frac{9\pi}{5}\]
Find the degree measure corresponding to the following radian measure:
\[- \frac{5\pi}{6}\]
Find the degree measure corresponding to the following radian measure:
\[\left( \frac{18\pi}{5} \right)\]
Find the degree measure corresponding to the following radian measure:
(−3)c
Find the degree measure corresponding to the following radian measure:
11c
Find the degree measure corresponding to the following radian measure:
1c
Find the radian measure corresponding to the following degree measure: −56°
Find the radian measure corresponding to the following degree measure: 135°
Find the radian measure corresponding to the following degree measure: −300°
Find the radian measure corresponding to the following degree measure: 7° 30'
Find the radian measure corresponding to the following degree measure: 125° 30'
Find the magnitude, in radians and degrees, of the interior angle of a regular octagon.
Let the angles of the quadrilateral be \[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ \text{ and }\left( a + 3d \right)^\circ\]
We know: \[a - 3d + a - d + a + d + a - 2d = 360\]
\[ \Rightarrow 4a = 360\]
\[ \Rightarrow a = 90\]
We have:
Greatest angle = 120°
Now,
\[a + 3d = 120\]
\[ \Rightarrow 90 + 3d = 120\]
\[ \Rightarrow 3d = 30\]
\[ \Rightarrow d = 10\]
Hence,
\[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ\text{ and }\left( a + 3d \right)^\circ\] are
Angles of the quadrilateral in radians =
The angle in one regular polygon is to that in another as 3 : 2 and the number of sides in first is twice that in the second. Determine the number of sides of two polygons.
The number of sides of two regular polygons are as 5 : 4 and the difference between their angles is 9°. Find the number of sides of the polygons.
A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° in a distance of 40 metres?
Find the length which at a distance of 5280 m will subtend an angle of 1' at the eye.
If D, G and R denote respectively the number of degrees, grades and radians in an angle, the
The angle between the minute and hour hands of a clock at 8:30 is
At 3:40, the hour and minute hands of a clock are inclined at
If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, than the ratio of the radii of the circles is
A circular wire of radius 7 cm is cut and bent again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is
The radius of the circle whose arc of length 15 π cm makes an angle of \[\frac{3\pi}{4}\] radian at the centre is
Find the value of `sqrt(3)` cosec 20° – sec 20°
State whether the statement is True or False? Also give justification.
The equality sinA + sin2A + sin3A = 3 holds for some real value of A.
State whether the statement is True or False? Also give justification.
Sin10° is greater than cos10°
State whether the statement is True or False? Also give justification.
One value of θ which satisfies the equation sin4θ - 2sin2θ - 1 lies between 0 and 2π.
