Advertisements
Advertisements
Question
Show that:
(ii) `(cos30^0+sin 60^0)/(1+sin30^0+cos60^0)=cos 30^0`
Solution
LHS =`(cos30^0+sin 60^0)/(1+sin30^0+cos60^0) = ((sqrt(3)/2+sqrt(3)/2))/(1+1/2+1/2)=((sqrt(3)+sqrt(3))/2)/((2+1+1)/2)=sqrt(3)/2`
Also, RHS = cos `30^0=sqrt(3)/2`
Hence, LHS = RHS
∴`(cos30^0+sin 60^0)/(1+sin30^0+cos60^0)=cos 30^0`
APPEARS IN
RELATED QUESTIONS
Given 15 cot A = 8. Find sin A and sec A.
In right angled triangle ΔABC at B, ∠A = ∠C. Find the values of sin A sin B + cos A cos B
If sin θ = ` (a^2 - b^2)/(a^2+b^2)`find all the values of all T-ratios of θ .
If ∠A and ∠B are acute angles such that sin A = Sin B prove that ∠A = ∠B.
In the adjoining figure, ΔABC is right-angled at B and ∠A = 300. If BC = 6cm, find (i) AB, (ii) AC.
Given: cos A = 0.6; find all other trigonometrical ratios for angle A.
In rhombus ABCD, diagonals AC and BD intersect each other at point O.
If cosine of angle CAB is 0.6 and OB = 8 cm, find the lengths of the side and the diagonals of the rhombus.
If sin A = `(sqrt3)/(2)` and cos B = `(sqrt3)/(2)` , find the value of : `(tan"A" – tan"B")/(1+tan"A" tan"B")`
In a right-angled triangle PQR, ∠PQR = 90°, QS ⊥ PR and tan R =`(5)/(12)`, find the value of sin ∠PQS
From the given figure, prove that θ + ∅ = 90°. Also prove that there are two other right angled triangles. Find sin α, cos β and tan ∅
