Grade 10Trigonometry
If cosA+cosB=1/2.and sinA+sinB=1/4.then tan(A/2+B/2)
1 Answer
Arun
Approved Tutor Answer8 Years agoDear student
cosA + cosB =1/2 & sinA+ sinB = 1/4
now cosA + cosB = 2 cos(A +B)/2 cos(A-B)/2 = 1/2--------------(I)
sinA + sinB = 2 sin(A+B)/2 cos(A- B)/2 = 1/4---------------(II)
dividing (I) by (II) we have
(cosA+cosB)/( sinA +sinB)= 1/2/1/4 = 2
or cot( A+B)/2 = 2
or tan (A+B)/2 = 1/2
now cosA + cosB = 2 cos(A +B)/2 cos(A-B)/2 = 1/2--------------(I)
sinA + sinB = 2 sin(A+B)/2 cos(A- B)/2 = 1/4---------------(II)
dividing (I) by (II) we have
(cosA+cosB)/( sinA +sinB)= 1/2/1/4 = 2
or cot( A+B)/2 = 2
or tan (A+B)/2 = 1/2
Regards
Arun (askIITians forum expert)
Other Related Questions on trigonometry
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
Last Activity: 3 Years ago
- Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
- Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
trigonometry
Last Activity: 4 Years ago
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
Last Activity: 4 Years ago
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥
trigonometry
Last Activity: 4 Years ago