Advertisements
Advertisements
Question
Prove that `(sec8 theta - 1)/(sec4 theta - 1) = (tan8 theta)/(tan2 theta)`
Advertisements
Solution
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
RELATED QUESTIONS
Find the radian measure corresponding to the following degree measure:
25°
Find the radian measure corresponding to the following degree measure:
– 47° 30'
Find the radian measure corresponding to the following degree measure:
240°
Find the degree measure corresponding to the following radian measure `(use pi = 22/7)`
`11/16`
Find the degree measure corresponding to the following radian measure (Use `pi = 22/7`)
-4
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
15 cm
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
21 cm
Find the degree measure corresponding to the following radian measure:
\[- \frac{5\pi}{6}\]
Find the degree measure corresponding to the following radian measure:
11c
Find the radian measure corresponding to the following degree measure:
300°
Find the radian measure corresponding to the following degree measure: −56°
Find the radian measure corresponding to the following degree measure: −300°
Find the radian measure corresponding to the following degree measure: 7° 30'
One angle of a triangle \[\frac{2}{3}\] x grades and another is \[\frac{3}{2}\] x degrees while the third is \[\frac{\pi x}{75}\] radians. Express all the angles in degrees.
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 angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.
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.
The radius of a circle is 30 cm. Find the length of an arc of this circle, if the length of the chord of the arc is 30 cm.
A railway train is travelling on a circular curve of 1500 metres radius at the rate of 66 km/hr. Through what angle has it turned in 10 seconds?
If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii.
If the angles of a triangle are in A.P., then the measures of one of the angles in radians is
The angle between the minute and hour hands of a clock at 8:30 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
A circular wire of radius 3 cm is cut and bent so as to lie along the circumference of a hoop whose radius is 48 cm. Find the angle in degrees which is subtended at the centre of hoop.
If θ lies in the second quadrant, then show that `sqrt((1 - sin theta)/(1 + sin theta)) + sqrt((1 + sin theta)/(1 - sin theta))` = −2sec θ
Find the value of tan 9° – tan 27° – tan 63° + tan 81°
The value of tan1° tan2° tan3° ... tan89° is ______.
State whether the statement is True or False? Also give justification.
`cos (2pi)/15 cos (4pi)/15 cos (8pi)/15 cos (16pi)/15 = 1/16`
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.
