Advertisements
Advertisements
Question
Write all the other trigonometric ratios of ∠A in terms of sec A.
Solution
(i) `sin A = sin A /1`
= `(sin A ÷ cos A)/(1÷ cos A)`
= `(sin A/cosA)/(1/cosA)`
= `tan A/sec A`
= `sqrt( tan^2 A)/sec A`
= `sqrt(sec^2A-1)/(secA)`
(ii) `cos A = 1/(sec A)`
(iii) `tan A = sqrt(tan^2 A) = sqrt(sec^2 A-1)`
(iv) `cosec A = 1/sinA = secA/sqrt(sec^2A-1)`
(v) `cot A = (cos A)/(sin A)`
= `(1/(secA))/(sqrt(sec^2A-1)/secA)`
= `1/(sqrt(sec^2A-1))`
APPEARS IN
RELATED QUESTIONS
If the angle θ= –60º, find the value of cosθ.
If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A
if `sqrt3 tan theta = 3 sin theta` find the value of `sin^2 theta - cos^2 theta`
Solve.
`tan47/cot43`
For triangle ABC, show that : `sin (A + B)/2 = cos C/2`
Evaluate:
`2 tan57^circ/(cot33^circ) - cot70^circ/(tan20^circ) - sqrt(2) cos45^circ`
Evaluate:
`(cot^2 41^circ)/(tan^2 49^circ) - 2 sin^2 75^circ/cos^2 15^circ`
Find the value of x, if sin 2x = 2 sin 45° cos 45°
Use tables to find sine of 47° 32'
Use tables to find sine of 10° 20' + 20° 45'
Use tables to find cosine of 9° 23’ + 15° 54’
Prove that:
tan (55° - A) - cot (35° + A)
If A and B are complementary angles, prove that:
`(sinA + sinB)/(sinA - sinB) + (cosB - cosA)/(cosB + cosA) = 2/(2sin^2A - 1)`
If 0° < A < 90°; find A, if `(cos A )/(1 - sin A) + (cos A)/(1 + sin A) = 4`
If the angle θ = –45° , find the value of tan θ.
Write the acute angle θ satisfying \[\cos B = \frac{3}{5}\]
Write the value of cos 1° cos 2° cos 3° ....... cos 179° cos 180°.
Write the value of tan 10° tan 15° tan 75° tan 80°?
If θ is an acute angle such that \[\cos \theta = \frac{3}{5}, \text{ then } \frac{\sin \theta \tan \theta - 1}{2 \tan^2 \theta} =\] \[\cos \theta = \frac{3}{5}, \text{ then } \frac{\sin \theta \tan \theta - 1}{2 \tan^2 \theta} =\]
If \[\frac{160}{3}\] \[\tan \theta = \frac{a}{b}, \text{ then } \frac{a \sin \theta + b \cos \theta}{a \sin \theta - b \cos \theta}\]
If 16 cot x = 12, then \[\frac{\sin x - \cos x}{\sin x + \cos x}\]
If 3 cos θ = 5 sin θ, then the value of
The value of cos2 17° − sin2 73° is
The value of cos 1° cos 2° cos 3° ..... cos 180° is
If A + B = 90°, then \[\frac{\tan A \tan B + \tan A \cot B}{\sin A \sec B} - \frac{\sin^2 B}{\cos^2 A}\]
\[\frac{1 - \tan^2 45°}{1 + \tan^2 45°}\] is equal to
Prove the following.
tan4θ + tan2θ = sec4θ - sec2θ
A, B and C are interior angles of a triangle ABC. Show that
sin `(("B"+"C")/2) = cos "A"/2`
A, B and C are interior angles of a triangle ABC. Show that
If ∠A = 90°, then find the value of tan`(("B+C")/2)`
Express the following in term of angles between 0° and 45° :
cos 74° + sec 67°
Evaluate:
3 cos 80° cosec 10°+ 2 sin 59° sec 31°
Evaluate: `(cot^2 41°)/(tan^2 49°) - 2 (sin^2 75°)/(cos^2 15°)`
Find the value of the following:
`((cos 47^circ)/(sin 43^circ))^2 + ((sin 72^circ)/(cos 18^circ))^2 - 2cos^2 45^circ`
Find the value of the following:
tan 15° tan 30° tan 45° tan 60° tan 75°
If tan θ = cot 37°, then the value of θ is
If sin 3A = cos 6A, then ∠A = ?
2(sin6 θ + cos6 θ) – 3(sin4 θ + cos4 θ) is equal to ______.
