Question

Eliminate Q if sin Q + tan Q =p tan Q - sin Q =q

Answer 1

Answer:

sinQ=(p-q)/2, tanQ=(p+q)/2

Explanation:

tanQ+sinQ=p

(rearranging the given equation)

sinQ=p-tanQ.........(1)

tanQ-sinQ =q. . . . given

tanQ-(p-tanQ)=q . . . from (1)

2tanQ=p+q

tanQ=(p+q)/2....(2)

put in (1)

sinQ=p-(p+q)/2

sinQ= (2p-p-q)/2

sinQ=(p-q)/2

=>sinQ=(p-q)/2, tanQ=(p+q)/2

Answer 2

Answer:

tanQ+sinQ=p

(rearranging the given equation)

sinQ=p-tanQ.........(1)

tanQ-sinQ =q. . . . given

tanQ-(p-tanQ)=q . . . from (1)

2tanQ=p+q

tanQ=(p+q)/2....(2)

put in (1)

sinQ=p-(p+q)/2

sinQ= (2p-p-q)/2

sinQ=(p-q)/2

=>sinQ=(p-q)/2, tanQ=(p+q)/2

Explanation: