Advertisements
Advertisements
Question
Prove that:
4 (sin4 30° + cos4 60°) -3 (cos2 45° - sin2 90°) = 2
Solution
LHS = `4(sin^4 30°+ cos^4 60°)- 3(cos^2 45° – sin^2 90°)`
= `4[(1/2)^4 + (1/2)^4] – 3[(1/sqrt2)^2 + (1)^4]`
= `4[ (1)/(16) + (1)/(16) ] – 3[ (1)/(2) – 1]`
= `(4 xx 2 )/(16) + 3 xx (1)/(2)`
= 2
RHS = 2
LHS = RHS
APPEARS IN
RELATED QUESTIONS
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
Evaluate the following:
`(cos 45°)/(sec 30° + cosec 30°)`
Evaluate the following:
`(sin 30° + tan 45° – cosec 60°)/(sec 30° + cos 60° + cot 45°)`
State whether the following is true or false. Justify your answer.
sinθ = cosθ for all values of θ.
Evaluate the following :
`((sin 27^@)/(cos 63^@))^2 - (cos 63^@/sin 27^@)^2`
Express cos 75° + cot 75° in terms of angles between 0° and 30°.
If A, B, C are the interior angles of a triangle ABC, prove that
`tan ((C+A)/2) = cot B/2`
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: Cosec (65 + θ) – sec (25 – θ) – tan (55 – θ) + cot (35 + θ)
Evaluate: `(2sin 68)/cos 22 - (2 cot 15^@)/(5 tan 75^@) - (8 tan 45^@ tan 20^@ tan 40^@ tan 50^@ tan 70^@)/5`
prove that:
sin (2 × 30°) = `(2 tan 30°)/(1+tan^2 30°)`
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratios: sin 45°
find the value of: cos2 60° + sin2 30°
prove that:
tan (2 x 30°) = `(2 tan 30°)/(1– tan^2 30°)`
secθ . Cot θ= cosecθ ; write true or false
Without using tables, evaluate the following: sin60° sin30°+ cos30° cos60°
Without using tables, evaluate the following: sin230° sin245° + sin260° sin290°.
Without using tables, evaluate the following: cosec245° sec230° - sin230° - 4cot245° + sec260°.
Find the value of x in the following: cos2x = cos60° cos30° + sin60° sin30°
If A = 30° and B = 60°, verify that: `(sin("A" -"B"))/(sin"A" . sin"B")` = cotB - cotA
If A = B = 45°, verify that cos (A − B) = cos A. cos B + sin A. sin B
If sin(A +B) = 1(A -B) = 1, find A and B.
Verify the following equalities:
1 + tan2 30° = sec2 30°
Find the value of the following:
(sin 90° + cos 60° + cos 45°) × (sin 30° + cos 0° – cos 45°)
If sin 30° = x and cos 60° = y, then x2 + y2 is
The value of `(2tan30^circ)/(1 - tan^2 30^circ)` is equal to
Evaluate: sin2 60° + 2tan 45° – cos2 30°.
