Advertisements
Advertisements
Question
Prove that `(sec8 theta - 1)/(sec4 theta - 1) = (tan8 theta)/(tan2 theta)`
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:
240°
Find the radian measure corresponding to the following degree measure:
520°
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 corresponding to the following radian measure (use `pi= 22/7`).
`(7pi)/6`
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
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:
1c
Find the radian measure corresponding to the following degree measure: −300°
Find the magnitude, in radians and degrees, of the interior angle of a regular octagon.
Find the magnitude, in radians and degrees, of the interior angle of a regular heptagon.
Find the magnitude, in radians and degrees, of the interior angle of a regular duodecagon.
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 angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.
Find the diameter of the sun in km supposing that it subtends an angle of 32' at the eye of an observer. Given that the distance of the sun is 91 × 106 km.
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.
If D, G and R denote respectively the number of degrees, grades and radians in an angle, the
At 3:40, the hour and minute hands of a clock are inclined at
If OP makes 4 revolutions in one second, the angular velocity in radians per second 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
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°
If tan θ = `(-4)/3`, then sin θ is ______.
Which of the following is correct?
[Hint: 1 radian = `180^circ/pi = 57^circ30^'` approx]
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°
