Question

If tanA=√3 -1/√3 +1 prove that cosA= √3 +1/ 2√2

Answer 1

Answer:

tanA=

2

−1, prove that

1+tan

2

A

tanA

=

4

2

ANSWER

tanA=

2

−1

tanA=

AB

BC

=

1

2−1

AC

2

=BA

2

+BC

2

=1

2

+(

2

−1)

2

=1+2−2

2

+1

AC=

4−2

2

sinA=

AC

BC

=

4−2

2

2

−1

cosA=

AC

AB

=

4−2

2

1

sinA×cosA=

4−2

2

2

−1

×

4−2

2

1

=

4−2

2

2

−1

=

2

2

(

2

−1)

2

−1

=

2

2

1

×

2

2

=

4

2

cosA×

cosA

sinA×cosA

=

4

2

Multiply numerator & denominator by cosA

sec

2

A

tanA

=

4

2

⇒

1+tan

2

A

tanA

=

4

2

Answer 2

.........IT MAY HELP YOU..........