Advertisements
Advertisements
Question
find the value of: cos2 60° + sec2 30° + tan2 45°
Solution
cos2 60° + sec2 30° + tan2 45° = `(1/2)^2 + (2/sqrt3)^2 + 1^2`
= `(1)/(4) + (4)/(3) + 1`
= `( 3 + 16 + 12)/(12)`
= `(31)/(12)`
= `2(7)/(12)`
APPEARS IN
RELATED QUESTIONS
If θ is an acute angle and sin θ = cos θ, find the value of 2 tan2 θ + sin2 θ – 1
Evaluate the following:
2tan2 45° + cos2 30° − sin2 60°
Evaluate the following:
`(cos 45°)/(sec 30° + cosec 30°)`
State whether the following is true or false. Justify your answer.
sin (A + B) = sin A + sin B
State whether the following are true or false. Justify your answer.
cot A is not defined for A = 0°.
Show that tan 48° tan 23° tan 42° tan 67° = 1
Evaluate the following:
`(sin 20^@)/(cos 70^@)`
Evaluate the following :
`cos 19^@/sin 71^@`
Evaluate the following :
`(sec 70^@)/(cosec 20^@) + (sin 59^@)/(cos 31^@)`
Evaluate the following :
sin 35° sin 55° − cos 35° cos 55°
Express each one of the following in terms of trigonometric ratios of angles lying between
0° and 45°
Sin 59° + cos 56°
Prove that:
sin 60° cos 30° + cos 60° . sin 30° = 1
prove that:
sin (2 × 30°) = `(2 tan 30°)/(1+tan^2 30°)`
Prove that:
4 (sin4 30° + cos4 60°) -3 (cos2 45° - sin2 90°) = 2
For any angle θ, state the value of: sin2 θ + cos2 θ
If A = 30o, then prove that :
2 cos2 A - 1 = 1 - 2 sin2A
If A = 30°;
show that:
cos 2A = cos4 A - sin4 A
Without using tables, evaluate the following: sin230° cos245° + 4tan230° + sin290° + cos20°
Without using tables, evaluate the following: 4(sin430° + cos460°) - 3(cos245° - sin290°).
Without using tables, find the value of the following: `(4)/(cot^2 30°) + (1)/(sin^2 60°) - cos^2 45°`
Find the value of x in the following: `2sin x/(2)` = 1
Find the value of x in the following: `sqrt(3)`tan 2x = cos60° + sin45° cos45°
If tan(A - B) = `(1)/sqrt(3)` and tan(A + B) = `sqrt(3)`, find A and B.
In ΔABC right angled at B, ∠A = ∠C. Find the value of:
(i) sinA cosC + cosA sinC
(ii) sinA sinB + cosA cosB
Verify the following equalities:
sin2 60° + cos2 60° = 1
Evaluate: `(5cos^2 60° + 4sec^2 30° - tan^2 45°)/(sin^2 30° + sin^2 60°)`