Advertisements
Advertisements
Question
Verify the following equalities:
sin 30° cos 60° + cos 30° sin 60° = sin 90°
Solution
sin 30° = `1/2`, cos 60° = `1/2`, cos 30° = `sqrt(3)/2`, sin 60° = `sqrt(3)/2`, sin 90° = 1
L.H.S = sin 30° cos 60° + cos 30° sin 60°
= `1/2 xx 1/2 + sqrt(3)/2 xx sqrt(3)/2`
= `1/4 + 3/4`
= `4/4`
= 1
R.H.S = sin 90° = 1
L.H.S = R.H.S
Hence it is proved.
APPEARS IN
RELATED QUESTIONS
Evaluate the following in the simplest form:
sin 60° cos 30° + cos 60° sin 30°
Evaluate the following:
`(sin 30° + tan 45° – cosec 60°)/(sec 30° + cos 60° + cot 45°)`
sin 2A = 2 sin A is true when A = ______.
Prove that
tan (55° − θ) − cot (35° + θ) = 0
If A =30o, then prove that :
sin 2A = 2sin A cos A = `(2 tan"A")/(1 + tan^2"A")`
Prove that:
cos2 30° - sin2 30° = cos 60°
If A =30o, then prove that :
cos 2A = cos2A - sin2A = `(1 – tan^2"A")/(1+ tan^2"A")`
If A = 30°;
show that:
`(1 + sin 2"A" + cos 2"A")/(sin "A" + cos"A") = 2 cos "A"`
If sinθ = cosθ and 0° < θ<90°, find the value of 'θ'.
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.
