Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org
  • Trigonometry
  • Trigonometric identities test
  • Sum to product formulas

Sum to product formulas

ans:
syntax error
C
DEL
ANS
±
(
)
÷
×
7
8
9
–
4
5
6
+
1
2
3
=
0
.
auto next question
evaluate answers
calculator
  • Question 1:
    1 pts
    		Express cos⁡2β−cos⁡8β\cos 2\beta -\cos 8\beta as a product.
    sin⁡10βsin⁡6β\sin 10\beta \sin 6\beta
    2sin⁡10βsin⁡6β2\sin 10\beta \sin 6\beta
    2sin⁡5βsin⁡3β2\sin 5\beta \sin 3\beta
    sin⁡5βsin⁡3β\sin 5\beta \sin 3\beta
  • Question 2:
    1 pts
    		Express sin⁡10M+sin⁡4M\sin 10M +\sin 4M as a product.

    −2sin⁡7Mcos⁡3M-2\sin 7M\cos 3M

    sin⁡7Mcos⁡3M\sin 7M\cos 3M

    12sin⁡7Mcos⁡3M\dfrac{1}{2} \sin 7M\cos 3M

    2sin⁡7Mcos⁡3M2\sin 7M\cos 3M

  • Question 3:
    1 pts
    		Express sin⁡(π4+α)+sin⁡(π4−α)\sin \left(\dfrac{\pi}{4}+\alpha\right)+\sin \left(\dfrac{\pi}{4}-\alpha\right) as a product.

    2sin⁡α\sqrt{2}\sin \alpha

    2cos⁡α\sqrt{2}\cos \alpha

    cos⁡α\cos \alpha

    sin⁡α\sin \alpha

  • Question 4:
    1 pts
    		sin⁡(α+β)−sin⁡(α−β)=2cos⁡βsin⁡α\sin(\alpha+\beta)-\sin(\alpha-\beta)=2\cos \beta \sin\alpha
  • Question 5:
    2 pts
    		Expresssin⁡20∘+cos⁡50∘\sin 20^{\circ}+\cos 50^{\circ} as a product.

    cos⁡40∘\cos 40^{\circ}

    cos⁡30∘\cos 30^{\circ}

    cos⁡20∘\cos 20^{\circ}

    cos⁡10∘\cos 10^{\circ}

  • Question 6:
    2 pts
    		Simplify the expression using sum to product formulas.
    sin⁡20∘+sin⁡34∘+sin⁡24∘+sin⁡30∘=\sin 20^{\circ}+ \sin 34^{\circ}+\sin 24^{\circ}+\sin 30^{\circ}=
  • Question 7:
    2 pts
    		Express cos⁡α+cos⁡3α+cos⁡5α+cos⁡7α\cos \alpha+\cos 3\alpha+\cos 5\alpha+\cos 7\alpha as a product.
    cos⁡αcos⁡2αcos⁡4α\cos\alpha \cos 2\alpha \cos 4\alpha
    4cos⁡αcos⁡2αcos⁡4α4\cos\alpha \cos 2\alpha \cos 4\alpha
    4cos⁡αcos⁡6αcos⁡8α4\cos\alpha \cos 6\alpha \cos 8\alpha
    none of these
  • Question 8:
    2 pts
    		sin⁡75∘+sin⁡15∘=62\sin 75^{\circ}+\sin 15^{\circ}=\dfrac{\sqrt{6}}{2}
  • Question 9:
    3 pts
    		Find the exact value of the expression.1+cos⁡x1+\cos x

    2cos⁡2x2\cos^{2} x

    2tan⁡2(x2)2\tan^{2}\left(\frac{x}{2}\right)

    2sin⁡2(x2)2\sin^{2}\left(\frac{x}{2}\right)

    2cos⁡2(x2)2\cos^{2}\left(\frac{x}{2}\right)

  • Question 10:
    3 pts
    		Find the exact value of the expression.
    sec⁡7∘(sin⁡47∘+sin⁡61∘−sin⁡11∘−sin⁡25∘)= \sec7^{\circ}(\sin 47^{\circ}+\sin 61^{\circ}-\sin 11^{\circ}-\sin25^{\circ})=
  • Question 11:
    3 pts
    		Find the exact value of the expression.
    cos⁡40∘+cos⁡40∘−cos⁡20∘sin⁡20∘=\dfrac{\cos 40^{\circ} + \cos 40^{\circ}-\cos 20^{\circ}}{\sin 20^{\circ}}=
  • Question 12:
    3 pts
    		Express as a product. tan⁡40∘+cot⁡40∘\tan 40^{\circ}+\cot 40^{\circ}
    2cos⁡20∘\dfrac{2}{\cos 20^{\circ}}
    2cos⁡10∘\dfrac{2}{\cos 10^{\circ}}
    1cos⁡10∘\dfrac{1}{\cos 10^{\circ}}
    2sin⁡10∘\dfrac{2}{\sin 10^{\circ}}

Angle Measurement

Right triangle

Unit circle

Trigonometric identities