Advertisements
Advertisements
Question
Without using tables, find the value of the following: `(tan45°)/("cosec"30°) + (sec60°)/(cot45°) - (5sin90°)/(2cos0°)`
Solution
`(tan45°)/("cosec"30°) + (sec60°)/(cot45°) - (5sin90°)/(2cos0°)`
= `(1)/(2) + (2)/(1) - (5 xx 1)/(2 xx 1)`
= `(1)/(2) + (2)/(1) - (5)/(2)`
= `(1 + 4 - 5)/(2)`
= 0.
APPEARS IN
RELATED QUESTIONS
If A, B and C are interior angles of a triangle ABC, then show that `\sin( \frac{B+C}{2} )=\cos \frac{A}{2}`
Show that:
(i) `2(cos^2 45º + tan^2 60º) – 6(sin^2 45º – tan^2 30º) = 6`
(ii) `2(cos^4 60º + sin^4 30º) – (tan^2 60º + cot^2 45º) + 3 sec^2 30º = 1/4`
Find the value of x in the following :
tan 3x = sin 45º cos 45º + sin 30º
Find the value of θ in each of the following :
(i) 2 sin 2θ = √3 (ii) 2 cos 3θ = 1
State whether the following is true or false. Justify your answer.
The value of cos θ increases as θ increases.
Express each one of the following in terms of trigonometric ratios of angles lying between
0° and 45°
Sin 59° + cos 56°
If Sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A =?
Prove that `cos 80^@/sin 10^@ + cos 59^@ cosec 31^@ = 2`
Prove the following
sin (50° − θ) − cos (40° − θ) + tan 1° tan 10° tan 20° tan 70° tan 80° tan 89° = 1
Evaluate: `4(sin^2 30 + cos^4 60^@) - 2/3 3[(sqrt(3/2))^2 . [1/sqrt2]^2] + 1/4 (sqrt3)^2`
Find the value of:
tan2 30° + tan2 45° + tan2 60°
If `sqrt3` = 1.732, find (correct to two decimal place) the value of sin 60o
Evaluate:
`(cos3"A" – 2cos4"A")/(sin3"A" + 2sin4"A")` , when A = 15°
If tan (A + B) = 1 and tan(A-B)`=1/sqrt3` , 0° < A + B < 90°, A > B, then find the values of A and B.
Prove that:
3 cosec2 60° - 2 cot2 30° + sec2 45° = 0
prove that:
cos (2 x 30°) = `(1 – tan^2 30°)/(1+tan^2 30°)`
secθ . Cot θ= cosecθ ; write true or false
Without using tables, evaluate the following sec45° sin45° - sin30° sec60°.
Without using tables, evaluate the following: cosec330° cos60° tan345° sin290° sec245° cot30°.
Without using tables, evaluate the following: 4(sin430° + cos460°) - 3(cos245° - sin290°).
Without using tables, find the value of the following: `(sin30°)/(sin45°) + (tan45°)/(sec60°) - (sin60°)/(cot45°) - (cos30°)/(sin90°)`
Without using tables, find the value of the following: `(4)/(cot^2 30°) + (1)/(sin^2 60°) - cos^2 45°`
Prove that : sec245° - tan245° = 1
If A = 30° and B = 60°, verify that: sin (A + B) = sin A cos B + cos A sin B
If sin(A - B) = sinA cosB - cosA sinB and cos(A - B) = cosA cosB + sinA sinB, find the values of sin15° and cos15°.
The value of `(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` is
The value of cos1°. cos2°. cos3°. cos4°....................... cos90° is ______.
