Question

sin(60°+A)-cos(30°-A) equal to ​

Answer 1

ANSWER :-

0

GIVEN TO FIND THE VALUE OF :-

• sin(60°+A) - cos(30°-A)

SOLUTION :-

》 Expanding them by using formulae

• sin(A+B) = sinA cosB + sinB cosA
• cos(A-B) = cosA cosB + sinA sinB

= sin60° cosA + sinA cos60° - [ cos30° cosA + sin30° sinA]

》 As we know from Trigonometric table ,

• sin60° = ½
• cos30° = ½

= 1/2 cosA + sinA 1/2 -[ 1/2 cosA + 1/2 sinA]

= cosA/2 + sinA /2 -[ cosA/2 + sinA/2]

》 Opening the brackets

= cosA/2 + sinA/2 - cosA/2 - sinA/2

》 Keeping like terms together

= cosA/2 - cosA/2 + sinA/2 - sinA/2

》 All terms cancel each other

= 0

So, the value of sin(60°+A) - cos(30°-A) is 0

KNOW MORE :-

sin(A+B)= sinAcosB + sinBcosA

sin(A-B) = sinAcosB- sinBcosA

cos(A+B) = cosAcosB - sinAsinB

cos(A-B) = cosAcosB + sinAsinB

tan(A+B) = (tanA+tanB)/(1-tanAtanB)

tan(A-B) = (tanA-tanB)/(1+tanAtanB)

cot(A+B) = (cotB cotA -1)/(cotB + cotA)

cot(A-B) =( cotB cotA + 1)/(cotB-cotA)