The value of sin 20-cos 70-cos 20-sin 70-sin 23-co 23-cos 23- 23- is

The correct option is C 12 We know that sin (A) #10;cos B = sin (A+B) #160; #10; #10;And sin (A) = #160;1cosecA #160; #10;Also, ...

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Standard XII

Mathematics

Sin(A+B)Sin(A-B)

The value of ...

Question

The value of $\frac{sin 20^{\circ} cos 70^{\circ} + cos 20^{\circ} sin 70^{\circ}}{sin 23^{\circ} c o sec 23^{\circ} + cos 23^{\circ} sec 23^{\circ}}$ is

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\frac{1}{2}

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Solution

The correct option is C $\frac{1}{2}$
We know that $sin (A) cos B = sin (A + B)$

And $sin (A) = \frac{1}{c o s e c A}$
Also, $cos (A) = \frac{1}{s e c A}$

So, $\frac{sin 20^{0} cos 70^{0} + cos 20^{0} sin 70^{0}}{sin 23^{0} c o s e c 23^{0} + cos 23^{0} sec 23^{0}} = \frac{sin {(20}^{0} + 70^{0})}{1 + 1} = \frac{1}{2}$ (Since, $sin 90^{0} = 1$ )

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Similar questions

Q. Write the value of

|\begin{matrix} \sin 20 ° & - \cos 20 ° \\ \sin 70 ° & \cos 70 ° \end{matrix}|

Q. Evaluate:

cos 20^{\circ} cos 70^{\circ} - sin 20^{\circ} sin 70^{\circ}

Q. Prove that:
(i) cos 10° cos 30° cos 50° cos 70° =

\frac{3}{16}

(ii) cos 40° cos 80° cos 160° =

- \frac{1}{8}

(iii) sin 20° sin 40° sin 80° =

\frac{\sqrt{3}}{8}

(iv) cos 20° cos 40° cos 80° =

\frac{1}{8}

(v) tan 20° tan 40° tan 60° tan 80° = 3

(vi) tan 20° tan 30° tan 40° tan 80° = 1

(vii) sin 10° sin 50° sin 60° sin 70° =

\frac{\sqrt{3}}{16}

(viii) sin 20° sin 40° sin 60° sin 80° =

\frac{3}{16}

Prove that:
(i) $c o s 55^{\circ} + c o s 65^{\circ} + c o s 175^{\circ} = 0$
(ii) $s i n 50^{\circ} - s i n 70^{\circ} + s i n 10^{\circ} = 0$
(iii) $c o s 80^{\circ} + c o s 40^{\circ} - c o s 20^{\circ} = 0$
(iv) $c o s 20^{\circ} + c o s 100^{\circ} + c o s 140^{\circ} = 0$
(v) $s i n \frac{5 π}{18} - c o s \frac{4 π}{9} = \sqrt{3} s i n \frac{π}{9}$
(vi) $c o s \frac{π}{12} - s i n \frac{π}{12} = \frac{1}{\sqrt{2}}$
(vii) $s i n 80^{\circ} - c o s 70^{\circ} = c o s 50^{\circ}$
(viii) $s i n 51^{\circ} - c o s 81^{\circ} = c o s 21^{\circ}$

Find the value of ( $c o s 20^{\circ} - s i n 20^{\circ}$ ) (1+4 $s i n 20^{\circ} c o s 20^{\circ}$ )

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The value of sin20∘cos70∘+cos20∘sin70∘sin23∘cosec23∘+cos23∘sec23∘ is

The correct option is C 12We know that sin(A)cosB=sin(A+B) And sin(A)=1cosecA Also, cos(A)=1secA So, sin200cos700+cos200sin700sin230cosec230+cos230sec230=sin(200+700)1+1=12 (Since, sin900=1)

The value of $\frac{sin 20^{\circ} cos 70^{\circ} + cos 20^{\circ} sin 70^{\circ}}{sin 23^{\circ} c o sec 23^{\circ} + cos 23^{\circ} sec 23^{\circ}}$ is