Advertisements
Advertisements
Question
Without using trigonometric tables, prove that:
tan 71° − cot 19° = 0
Solution
LHS = tan 71° − cot 19°
= `tan (90^circ - 19^circ) - cot 19^circ`
= `cot 19^circ - cot 19^circ`
= 0
= RHS
APPEARS IN
RELATED QUESTIONS
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
(sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A
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.]
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`((1+tan^2A)/(1+cot^2A))=((1-tanA)/(1-cotA))^2=tan^2A`
Without using trigonometric tables, evaluate :
`tan 27^circ/cot 63^circ`
Without using trigonometric tables, evaluate :
`("cosec" 42^circ)/sec 48^circ`
Without using trigonometric tables, prove that:
tan266° − cot224° = 0
Prove that:
`cos 80^circ/(sin 10^circ) + cos 59^circ "cosec" 31^circ = 2`
Prove that:
`(2 "sin" 68^circ)/(cos 10^circ )- (2 cot 15^circ)/(5 tan 75^circ) = ((3 tan 45^circ t an 20^circ tan 40^circ tan 50^circ tan 70^circ)) /5= 1`
Prove that:
`sin 18^circ/(cos 72^circ )+ sqrt(3)(tan 10^circ tan 30^circ tan 40^circ tan50^circ tan 80^circ) `
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:
\[cot\theta \tan\left( 90° - \theta \right) - \sec\left( 90° - \theta \right)cosec\theta + \sqrt{3}\tan12° \tan60° \tan78° = 2\]
Prove that:
cot12° cot38° cot52° cot60° cot78° = \[\frac{1}{\sqrt{3}}\]
If sin 3 A = cos (A − 26°), where 3 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]
Prove the following:
`1/(1+sin^2theta) + 1/(1+cos^2theta) + 1/(1+sec^2theta) + 1/(1+cosec^2theta) = 2`
Without using trigonometric tables, find the value of (sin 72° + cos 18°)(sin 72° - cos 18°).
Solve : Sin2θ - 3sin θ + 2 = 0 .
If 5 tan θ = 4, find the value of `(5 sin θ + 3 cos θ)/(5 sin θ + 2 cos θ)`
