Advertisements
Advertisements
प्रश्न
If sec2A = cosec(A - 42°), where 2A is an acute angle, then find the value of A.
उत्तर
\[\sec2A = cosec\left( A - 42^\circ \right)\]
\[ \Rightarrow cosec\left( 90^\circ- 2A \right) = cosec\left( A - 42^\circ \right)\]
Comparing both sides, we get
\[90^\circ- 2A = A - 42^\circ\]
\[ \Rightarrow 2A + A = 90^\circ + 42^\circ\]
\[ \Rightarrow 3A = 132^\circ\]
\[ \Rightarrow A = \frac{132^\circ}{3}\]
\[ \therefore A = 44^\circ\]
Hence, the value of A is 44°
APPEARS IN
संबंधित प्रश्न
In the below given figure, a tower AB is 20 m high and BC, its shadow on the ground, is 20√3 m long. Find the sun’s altitude.
Evaluate without using trigonometric tables,
`sin^2 28^@ + sin^2 62^@ + tan^2 38^@ - cot^2 52^@ + 1/4 sec^2 30^@`
Without using trigonometrical tables, evaluate:
`cosec^2 57^circ - tan^2 33^circ + cos 44^circ cosec 46^circ - sqrt(2) cos 45^circ - tan^2 60^circ`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
(cosec A - sin A) (sec A - cos A) = `1/(tanA+cotA)`
[Hint: Simplify LHS and RHS separately.]
Without using trigonometric tables, evaluate :
`sin 16^circ/cos 74^circ`
Without using trigonometric tables, evaluate :
`cos 35^circ/sin 55^circ`
Without using trigonometric tables, prove that:
cosec 80° − sec 10° = 0
Without using trigonometric tables, prove that:
(sin72° + cos18°)(sin72° − cos18°) = 0
Prove that:
\[\frac{sin\theta \cos(90° - \theta)cos\theta}{\sin(90° - \theta)} + \frac{cos\theta \sin(90° - \theta)sin\theta}{\cos(90° - \theta)}\]
Prove that:
cot12° cot38° cot52° cot60° cot78° = \[\frac{1}{\sqrt{3}}\]
If tan 2 A = cot (A − 12°), where 2 A is an acute angle, find the value of A.
A man in a boat rowing away from a lighthouse 100 m high takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat in metres per minute [Use `sqrt3` = 1.732]
Without using tables evaluate: `(2tan 53°)/(cot 37°) - (cot 80°)/(tan 10°)`.
Solve the following equation: `(cos θ)/(1 - sin θ) + cos θ/(1 + sinθ) = 4`.
Using trigonometric table evaluate the following:
tan 25°45' + cot 45°25'.
Using trigonometric table evaluate the following:
sin 64°42' + cos 42°20'
The length of a shadow of a tower standing on a level plane is found to be 2y meters longer when the seen's altitude is 30° than when it was 45° prove that the height of the tower is y ( √3 + 1 ) meter.
Given that sin θ = `a/b` then cos θ is equal to ______.
The maximum value of `1/(cosec alpha)` is ______.
