Home
Class 12
MATHS
(sin 12^(@)) (sin 48^(@)) (sin 54^(@) ) ...

`(sin 12^(@)) (sin 48^(@)) (sin 54^(@) ) = ?`

A

`1/8`

B

`1/7`

C

`1/6`

D

`1/5`

लिखित उत्तर

Verified by Experts

The correct Answer is:
A
`LHS=``(sin 12^(@)) (sin 48^(@)) (sin 54^(@))`

`=1/2 xx(2 sin 12^(@)``sin 48^(@))xxsin 54^(@)`

`=1/2 xx[cos (12^(@)-48^@)``-cos (12^@ + 48^(@)]``xxsin 54^(@)`

चूंकि `2sinAsinB``=cos(A-B)-cos(A+B)`

`=1/2 xx[cos (-36^@)``-cos (60^(@))]``xx(sqrt5 + 1)/(4)`

चूंकि `sin 54^(@) ``=(sqrt5 + 1)/(4)``=cos36^@`

`=1/2 xx[cos (36^@)``-1/2]``xx(sqrt5 + 1)/(4)`

`=1/2 xx[(sqrt5 + 1)/(4)``-1/2]``xx(sqrt5 + 1)/(4)`

`=1/2 xx[(sqrt5 + 1- 2)/4]``xx(sqrt5 + 1)/(4)`

`=1/2 xx[(sqrt5 -1)/4]``xx(sqrt5 + 1)/(4)`

`=1/2 xx[((sqrt5)^2-1^2]/16]`

`=1/2 xx[(5-1]/16]``=1/2 xx[4/16]`

`=1/8``=RHS`

अतः सिद्ध हुआ।
Promotional Banner

टॉपर्स ने हल किए ये सवाल

  • त्रिकोणमितीय अनुपात एवं सर्वसमिकाएँ

    JEE Main & Advanced (Hindi Medium)|Exercise सत्य /असत्य|1 Videos

  • गणितीय आगमन का सिद्धांत

    JEE Main & Advanced (Hindi Medium)|Exercise विश्लेषणात्मक प्रश्न|9 Videos

  • त्रिकोणमितीय समीकरण

    JEE Main & Advanced (Hindi Medium)|Exercise एकल पूर्णांक प्रश्न|4 Videos