Question

sin A + cos A÷
sinA - cosA
+
sinA-cosA÷ sinA+cosA =
2÷ 1- cos²A​

Answer 1

Answer:

sinA−cosA

sinA+cosA

+

sinA+cosA

sinA−cosA

=

(sinA−cosA)(sinA+cosA)

(sinA+cosA)

2

+

(sinA−cosA)(sinA+cosA)

(sinA−cosA)

2

=

sin

2

A−cos

2

A

sin

2

A+cos

2

A+2sinAcosA+sin

2

A+cos

2

A−2sinAcosA

=

sin

2

A−cos

2

A

2

=

sin

2

A−(1−sin

2

A)

2

=

2sin

2

A−1

2

=

2(1−cos

2

A)−1

2

=

1−2co

View solution

Prove that

sin(A+B+C)+sin(−A+B+C)−sin(A−B+C)+sin(A+B−C)

cos(A+B+C)+cos(−A+B+C)+cos(A−B+C)+cos(A+B−C)

=