मराठी

The value of cos248∘-sin212∘ is ______.

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प्रश्न

The value of `cos^2 48^@ - sin^2 12^@` is ______.

पर्याय

  • `(sqrt5 + 1)/(2 sqrt2)`
  • `(sqrt5 + 1)/(5)`
  • `(sqrt5 - 1)/(8)`
  • `(sqrt5 + 1)/(8)`
MCQ
रिकाम्या जागा भरा
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उत्तर

The value of `cos^2 48^@ - sin^2 12^@` is `bbunderline((sqrt5 + 1)/(8))`.

Explanation:

\[\cos^2 48° - \sin^2 12°\]

\[ = \cos\left( 48° + 12° \right)\cos\left( 48° - 12° \right) \left[ \cos\left( A + B \right)\cos\left( A - B \right) = \cos^2 A - \sin^2 B \right]\]

\[ = \cos60° \cos36° \]

\[ = \frac{1}{2} \times \left( \frac{\sqrt{5} + 1}{4} \right)\]

\[ = \frac{\sqrt{5} + 1}{8}\]

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Values of Trigonometric Functions at Multiples and Submultiples of an Angle
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पाठ 9: Values of Trigonometric function at multiples and submultiples of an angle - Exercise 9.5 [पृष्ठ ४५]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 9 Values of Trigonometric function at multiples and submultiples of an angle
Exercise 9.5 | Q 38 | पृष्ठ ४५

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