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STD 11 - 3. trignometrical ratios,functions and identities — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 3. trignometrical ratios,functions and identities4 Marks
MCQ
The value of $cos\, 255^o + sin\, 195^o$ is
  • A
    $\frac{{\sqrt 3  - 1}}{{2\sqrt 2 }}\,$
  • B
    $\frac{{\sqrt 3  - 1}}{{\sqrt 2 }}\,$
  • ✓
    $-\frac{{\sqrt 3  - 1}}{{\sqrt 2 }}\,$
  • D
    $\frac{{\sqrt 3  + 1}}{{\sqrt 2 }}\,$
✓

Answer

Correct option: C.
$-\frac{{\sqrt 3  - 1}}{{\sqrt 2 }}\,$
c
Consider $\cos \,{255^o}\, + \,\sin \,{195^o}$

$ = \,\cos \,({270^o}\, - \,{15^o})\, + \,\sin \,({180^o} + {15^o})$

$ = \, - \,\sin \,{15^o}\, - \,\sin \,{15^o}$

$ = \, - \,2\,\sin \,{15^o}\, = \, - \,2\left( {\frac{{\sqrt 3  - 1}}{{2\sqrt 2 }}} \right)\, = \, - \,\left( {\frac{{\sqrt 3  - 1}}{{\sqrt 2 }}} \right)$

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