Question

Show that tan48° tan23° tan42° tan67°=1
​

Answer 1

Answer:

LHS

=tan 48°.tan 23°.tan 42°.tan 67°

=tan 48°.tan 42° .tan 23°.tan 67°

=tan (90°-42°).tan42°. tan(90°-67°).tan 67°

=cot42°.tan42°.cot67°.tan67°

=1×1=1=RHS proved

Answer 2

★Question★

Show that tan 48° tan 23° tan 42° tan 67°= 1

★Solution★

Taking L.H.S,

tan 48°tan 42°tan 23°tan 67°

= tan 48° tan(90° - 48°)tan 23° tan(90°-23°)

= tan 48°cot 48°tan 23°cot 23°

= (tan 48° × $\frac{1}{tan \: 48°})$ × ( tan 23° × $\frac{1}{tan \: 23°}$)

= 1×1

= 1

Therefore, L.H.S = R.H.S

Hence Proved

★Extra Information★

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.