Advertisements
Advertisements
Question
If sec A = cosec A and 0° ∠A ∠90°, state the value of A
Solution
sec A = cosec A
cos A = sin A
cos2A = sin2A
cos2 A = 1 – cos2A
2cos2A = 1
cos A = `(1)/(sqrt2)`
A = 45°
APPEARS IN
RELATED QUESTIONS
Using the formula, sin(A – B) = sinA cosB – cosA sinB, find the value of sin 15º
Evaluate the following:
`(cos 45°)/(sec 30° + cosec 30°)`
Evaluate the following:
`(5cos^2 60° + 4sec^2 30° - tan^2 45°)/(sin^2 30° + cos^2 30°)`
`(2 tan 30°)/(1+tan^2 30°)` = ______.
State whether the following is true or false. Justify your answer.
sinθ = cosθ for all values of θ.
State whether the following are true or false. Justify your answer.
cot A is not defined for A = 0°.
Evaluate cos 48° − sin 42°
Evaluate the following :
`cos 19^@/sin 71^@`
Evaluate the following
`sec 11^@/(cosec 79^@)`
Evaluate the following :
`(sec 70^@)/(cosec 20^@) + (sin 59^@)/(cos 31^@)`
Evaluate the following :
(sin 72° + cos 18°) (sin 72° − cos 18°)
Express cos 75° + cot 75° in terms of angles between 0° and 30°.
Prove that `cos 80^@/sin 10^@ + cos 59^@ cosec 31^@ = 2`
Evaluate: Cosec (65 + θ) – sec (25 – θ) – tan (55 – θ) + cot (35 + θ)
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
cot65° + tan49°
Evaluate:
`(cos3"A" – 2cos4"A")/(sin3"A" + 2sin4"A")` , when A = 15°
If A = B = 45° ,
show that:
sin (A - B) = sin A cos B - cos A sin B
find the value of: sin2 30° + cos2 30°+ cot2 45°
If `sqrt3` = 1.732, find (correct to two decimal place) the value of `(2)/(tan 30°)`
If A = 30o, then prove that :
2 cos2 A - 1 = 1 - 2 sin2A
If A = B = 45° ,
show that:
cos (A + B) = cos A cos B - sin A sin B
If A = 30°;
show that:
`(cos^3"A" – cos 3"A")/(cos "A") + (sin^3"A" + sin3"A")/(sin"A") = 3`
Without using tables, evaluate the following sec45° sin45° - sin30° sec60°.
Without using tables, find the value of the following: `(tan45°)/("cosec"30°) + (sec60°)/(cot45°) - (5sin90°)/(2cos0°)`
Prove that : sec245° - tan245° = 1
Find the value of x in the following: cos2x = cos60° cos30° + sin60° sin30°
Find the value of the following:
`(tan45^circ)/("cosec"30^circ) + (sec60^circ)/(cot45^circ) - (5sin90^circ)/(2cos0^circ)`
`(2/3 sin 0^circ - 4/5 cos 0^circ)` is equal to ______.