Advertisements
Advertisements
Question
If A = B = 45° ,
show that:
sin (A - B) = sin A cos B - cos A sin B
Solution
Given that A = B = 45°
LHS = sin (A – B)
= sin ( 45° – 45°)
= sin 0°
= 0
RHS = sin A cos B – cos A sin B
= sin 45° cos 45° – cos 45° sin 45°
= `(1)/(sqrt2) (1)/(sqrt2) – (1)/(sqrt2) (1)/(sqrt2)`
= 0
LHS = RHS
APPEARS IN
RELATED QUESTIONS
Evaluate the following in the simplest form: sin 60º cos 45º + cos 60º sin 45º
State whether the following is true or false. Justify your answer.
The value of cos θ increases as θ increases.
Evaluate cos 48° − sin 42°
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
cot 85° + cos 75°
If Sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A =?
Prove the following
sin θ sin (90° − θ) − cos θ cos (90° − θ) = 0
Prove the following
`(tan (90 - A) cot A)/(cosec^2 A) - cos^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
Evaluate:
`2/3 (cos^4 30° - sin^4 45°) - 3(sin^2 60° - sec^2 45°) + 1/4 cot^2 30°`.
Evaluate: `sin 50^@/cos 40^@ + (cosec 40^@)/sec 50^@ - 4 cos 50^@ cosec 40^@`
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
cosec54° + sin72°
Given A = 60° and B = 30°,
prove that : sin (A + B) = sin A cos B + cos A sin B
If tan (A + B) = 1 and tan(A-B)`=1/sqrt3` , 0° < A + B < 90°, A > B, then find the values of A and B.
find the value of: cosec2 60° - tan2 30°
Prove that:
cos 30° . cos 60° - sin 30° . sin 60° = 0
Prove that:
`((tan60° + 1)/(tan 60° – 1))^2 = (1+ cos 30°) /(1– cos 30°) `
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratio: cos 45°
For any angle θ, state the value of: sin2 θ + cos2 θ
If A = 30°;
show that:
`(1 – cos 2"A")/(sin 2"A") = tan"A"`
Without using tables, evaluate the following: sec30° cosec60° + cos60° sin30°.
Without using tables, evaluate the following: cosec245° sec230° - sin230° - 4cot245° + sec260°.
Without using table, find the value of the following:
`(sin30° - sin90° + 2cos0°)/(tan30° tan60°)`
Find the value of x in the following: `sqrt(3)`tan 2x = cos60° + sin45° cos45°
If sin(A - B) = sinA cosB - cosA sinB and cos(A - B) = cosA cosB + sinA sinB, find the values of sin15° and cos15°.
If sin(A - B) = `(1)/(2)` and cos(A + B) = `(1)/(2)`, find A and B.
Verify the following equalities:
cos 90° = 1 – 2sin2 45° = 2cos2 45° – 1
Verify cos3A = 4cos3A – 3cosA, when A = 30°
`(2/3 sin 0^circ - 4/5 cos 0^circ)` is equal to ______.
Evaluate: `(5 "cosec"^2 30^circ - cos 90^circ)/(4 tan^2 60^circ)`
