Advertisements
Advertisements
Question
State whether the following are true or false. Justify your answer.
The value of tan A is always less than 1.
Options
True
False
Advertisements
Solution
This statement is False.
Explanation:
Consider a ΔABC, right-angled at B.
tan A = `("Side opposite to ∠A")/("Side adjacent to ∠A")`
= `12/5`
But `12/5 > 1`
∴ tan A > 1
So, tan A < 1 is not always true.
Hence, the given statement is false.
A tangent of an angle is the ratio of sides other than hypotenuse, which may be equal or unequal to each other.
APPEARS IN
RELATED QUESTIONS
If cot θ = `7/8`, evaluate cot2 θ.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos theta = 7/25`
If 3 tan θ = 4, find the value of `(4cos theta - sin theta)/(2cos theta + sin theta)`
If `cos θ = 12/13`, show that `sin θ (1 - tan θ) = 35/156`.
If `cot theta = 1/sqrt3` show that `(1 - cos^2 theta)/(2 - sin^2 theta) = 3/5`
Evaluate the following
cos2 30° + cos2 45° + cos2 60° + cos2 90°
Evaluate the following
tan2 30° + tan2 60° + tan2 45°
Evaluate the Following
cosec3 30° cos 60° tan3 45° sin2 90° sec2 45° cot 30°
Evaluate the Following
(cos 0° + sin 45° + sin 30°)(sin 90° − cos 45° + cos 60°)
Evaluate the Following:
`(tan^2 60^@ + 4 cos^2 45^@ + 3 sec^2 30^@ + 5 cos^2 90)/(cosec 30^@ + sec 60^@ - cot^2 30^@)`
Evaluate the Following
`sin 30^2/sin 45^@ + tan 45^@/sec 60^@ - sin 60^@/cot 45^@ - cos 30^@/sin 90^@`
Find the value of x in the following :
`sqrt3 sin x = cos x`
If `sqrt2 sin (60° – α) = 1` then α is ______.
If cos A + cos² A = 1, then sin² A + sin4 A is equal to ______.
If sin A = `1/2`, then the value of cot A is ______.
In ΔABC, ∠ABC = 90° and ∠ACB = θ. Then write the ratios of sin θ and tan θ from the figure.
If sec θ = `1/2`, what will be the value of cos θ?
Let tan9° = `(1 - sqrt((sqrt(5)k)/m))k` where k = `sqrt(5) + 1` then m is equal to ______.
If b = `(3 + cot π/8 + cot (11π)/24 - cot (5π)/24)`, then the value of `|bsqrt(2)|` is ______.
If θ is an acute angle of a right angled triangle, then which of the following equation is not true?
