Advertisements
Advertisements
प्रश्न
State whether the following are true or false. Justify your answer.
sec A = `12/5` for some value of angle A.
विकल्प
True
False
उत्तर
This statement is True.
Explanation:
sec A = `12/5`
`"Hypotenuse"/"Side adjacent to ∠A" - 12/5`
`("AC")/("AB") = (12/5)`
Let AC be 12k, AB will be 5k, where k is a positive integer.
Applying Pythagoras theorem in ΔABC, we obtain
AC2 = AB2 + BC2
(12k)2 = (5k)2 + BC2
144k2 = 25k2 + BC2
BC2 = 119k2
BC = 10.9k
It can be observed that for given two sides AC = 12k and AB = 5k,
BC should be such that,
AC − AB < BC < AC + AB
12k − 5k < BC < 12k + 5k
7k < BC < 17 k
However, BC = 10.9k
Clearly, such a triangle is possible and hence, such value of sec A is possible.
Hence, the given statement is true.
संबंधित प्रश्न
If cot θ =` 7/8` evaluate `((1+sin θ )(1-sin θ))/((1+cos θ)(1-cos θ))`
State whether the following are true or false. Justify your answer.
cos A is the abbreviation used for the cosecant of angle A.
State whether the following are true or false. Justify your answer.
cot A is the product of cot and A.
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
tan θ = 11
If `tan theta = a/b`, find the value of `(cos theta + sin theta)/(cos theta - sin theta)`
If tan θ = `a/b` prove that `(a sin theta - b cos theta)/(a sin theta + b cos theta) = (a^2 - b^2)/(a^2 + b^2)`
if `cos theta = 3/5`, find the value of `(sin theta - 1/(tan theta))/(2 tan theta)`
if `sec A = 17/8` verify that `(3 - 4sin^2A)/(4 cos^2 A - 3) = (3 - tan^2 A)/(1 - 3 tan^2 A)`
Evaluate the following
sin 45° sin 30° + cos 45° cos 30°
Evaluate the following
`sin^2 30° cos^2 45 ° + 4 tan^2 30° + 1/2 sin^2 90° − 2 cos^2 90° + 1/24 cos^2 0°`
Evaluate the following:
(cosec2 45° sec2 30°)(sin2 30° + 4 cot2 45° − sec2 60°)
Evaluate the Following:
`tan 45^@/(cosec 30^@) + sec 60^@/cot 45^@ - (5 sin 90^@)/(2 cos 0^@)`
Find the value of x in each of the following :
cos x = cos 60º cos 30º + sin 60º sin 30º
Find the value of x in the following :
cos 2x = cos 60° cos 30° + sin 60° sin 30°
In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC
If cos (81 + θ)° = sin`("k"/3 - theta)^circ` where θ is an acute angle, then the value of k is ______.
`(sin theta)/(1 + cos theta)` is ______.
The value of cos 0°. cos 1°. cos 2°. cos 3°… cos 89° cos 90° is ______.
