Advertisements
Advertisements
प्रश्न
Without using tables, evaluate the following sec45° sin45° - sin30° sec60°.
उत्तर
sec45° sin45° - sin30° sec60°.
cos45° = `(1)/sqrt(2)`
⇒ sec45° = `sqrt(2)`
sin45° = `(1)/sqrt(2)`
sin30° = `(1)/(2)`
cos60° = `(1)/(2)`
⇒ sec60° = 2
sec45° sin45° - sin30° sec60°
= `sqrt(2) xx (1)/sqrt(2) - (1)/sqrt(2) xx 2`
= 1 - 1
= 0.
APPEARS IN
संबंधित प्रश्न
Evaluate the following expression:
(i) `tan 60º cosec^2 45º + sec^2 60º tan 45º`
(ii) `4cot^2 45º – sec^2 60º + sin^2 60º + cos^2 90º.`
sin 2A = 2 sin A is true when A = ______.
State whether the following is true or false. Justify your answer.
The value of cos θ increases as θ increases.
State whether the following are true or false. Justify your answer.
cot A is not defined for A = 0°.
Evaluate the following
`sec 11^@/(cosec 79^@)`
Evaluate the following :
`((sin 49^@)/(cos 41^@))^2 + (cos 41^@/(sin 49^@))^2`
Evaluate the following :
`tan 35^@/cot 55^@ + cot 78^@/tan 12^@ -1`
Prove that sin 48° sec 42° + cos 48° cosec 42° = 2
Prove that `cos 80^@/sin 10^@ + cos 59^@ cosec 31^@ = 2`
Prove the following :
`(cos(90°−A) sin(90°−A))/tan(90°−A) - sin^2 A = 0`
Prove the following
sin (50° − θ) − cos (40° − θ) + tan 1° tan 10° tan 20° tan 70° tan 80° tan 89° = 1
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
sec78° + cosec56°
If A = 30°;
show that:
sin 3 A = 4 sin A sin (60° - A) sin (60° + A)
find the value of :
3sin2 30° + 2tan2 60° - 5cos2 45°
Prove that:
3 cosec2 60° - 2 cot2 30° + sec2 45° = 0
prove that:
tan (2 x 30°) = `(2 tan 30°)/(1– tan^2 30°)`
If A =30o, then prove that :
sin 3A = 3 sin A - 4 sin3A.
If A = 30°;
show that:
4 cos A cos (60° - A). cos (60° + A) = cos 3A
Without using tables, evaluate the following: sin230° cos245° + 4tan230° + sin290° + cos20°
Without using tables, evaluate the following: (sin90° + sin45° + sin30°)(sin90° - cos45° + cos60°).
Without using tables, find the value of the following: `(tan45°)/("cosec"30°) + (sec60°)/(cot45°) - (5sin90°)/(2cos0°)`
Prove that : sec245° - tan245° = 1
Without using table, find the value of the following: `(tan^2 60° + 4cos^2 45° + 3sec^2 30° + 5cos90°)/(cosec30° + sec60° - cot^2 30°)`
Verify the following equalities:
sin 30° cos 60° + cos 30° sin 60° = sin 90°
Find the value of the following:
`(tan45^circ)/("cosec"30^circ) + (sec60^circ)/(cot45^circ) - (5sin90^circ)/(2cos0^circ)`
Verify cos3A = 4cos3A – 3cosA, when A = 30°
If sin 30° = x and cos 60° = y, then x2 + y2 is
If sin(A + B) = 1 and cos(A – B)= `sqrt(3)/2`, 0° < A + B ≤ 90° and A > B, then find the measures of angles A and B.
If A and B are acute angles such that sin (A – B) = 0 and 2 cos (A + B) – 1 = 0, then find angles A and B.
