Advertisements
Advertisements
Question
The value of tan 10° tan 15° tan 75° tan 80° is
Options
−1
0
1
None of these
Solution
Here we have to find: ` tan 10° tan 15° tan75° tan 80° `
Now
`tan 10° tan 15° tan75° tan 80° `
=`tan (90°-80°) tan (90°-75°) tan 80° `
= `cot 80° cot 75° tan 75° tan 80°`
=`(cot 80° tan 80°)(cot 75° tan 75°)`
=`1xx1` ` [ "since" cot θ tanθ =1]`
=` 1`
APPEARS IN
RELATED QUESTIONS
Without using trigonometric tables, evaluate the following:
`( i)\frac{\cos37^\text{o}}{\sin53^\text{o}}\text{ }(ii)\frac{\sin41^\text{o}}{\cos 49^\text{o}}(iii)\frac{\sin30^\text{o}17'}{\cos59^\text{o}\43'}`
If A, B, C are the interior angles of a triangle ABC, prove that `\tan \frac{B+C}{2}=\cot \frac{A}{2}`
Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.
What is the value of (cos2 67° – sin2 23°)?
if `tan theta = 12/5` find the value of `(1 + sin theta)/(1 -sin theta)`
solve.
sec2 18° - cot2 72°
Evaluate:
14 sin 30° + 6 cos 60° – 5 tan 45°
Evaluate:
`2(tan35^@/cot55^@)^2 + (cot55^@/tan35^@)^2 - 3(sec40^@/(cosec50^@))`
Evaluate:
sin 27° sin 63° – cos 63° cos 27°
Prove that:
sin (28° + A) = cos (62° – A)
Find A, if 0° ≤ A ≤ 90° and 2 cos2 A – 1 = 0
What is the maximum value of \[\frac{1}{\sec \theta}\]
If A + B = 90° and \[\cos B = \frac{3}{5}\] what is the value of sin A?
If \[\tan A = \frac{5}{12}\] \[\tan A = \frac{5}{12}\] find the value of (sin A + cos A) sec A.
The value of
If A + B = 90°, then \[\frac{\tan A \tan B + \tan A \cot B}{\sin A \sec B} - \frac{\sin^2 B}{\cos^2 A}\]
The value of 3 sin 70° sec 20° + 2 sin 49° sec 51° is
In ∆ABC, `sqrt(2)` AC = BC, sin A = 1, sin2A + sin2B + sin2C = 2, then ∠A = ? , ∠B = ?, ∠C = ?
If A, B and C are interior angles of a ΔABC then `cos (("B + C")/2)` is equal to ______.
The value of (tan1° tan2° tan3° ... tan89°) is ______.
