Question 3 iiEvaluate-ii sin 25- cos 65- - cos 25- sin65-

(ii) sin 25^∘ cos 65^∘ + cos 25^∘ sin 65^∘ = sin(90^∘ 65^∘) cos 65^∘+cos(90^∘ 65^∘) sin 65^∘ = cos 65^∘ cos 65^∘+ sin 65^∘ sin65^∘ = cos^265^∘+ sin^265^∘ = 1 ...

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Standard XI

Mathematics

Sum of Trigonometric Ratios in Terms of Their Product

Question 3 ii...

Question

Question 3 (ii)
Evaluate:
(ii) $s i n 25^{\circ} c o s 65^{\circ} + c o s 25^{\circ} s i n 65^{\circ}$

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Solution

(ii) $s i n 25^{\circ} c o s 65^{\circ} + c o s 25^{\circ} s i n 65^{\circ}$
$= s i n (90^{\circ} - 65^{\circ}) c o s 65^{\circ} + c o s (90^{\circ} - 65^{\circ}) s i n 65^{\circ}$
$= c o s 65^{\circ} c o s 65^{\circ} + s i n 65^{\circ} s i n 65^{\circ}$
$= c o s^{2} 65^{\circ} + s i n^{2} 65^{\circ} = 1$

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Q. Question 3 (ii)
Evaluate:
(ii)

s i n 25^{\circ} c o s 65^{\circ} + c o s 25^{\circ} s i n 65^{\circ}

{s i n 25}^{\circ} c o s 65 + {c o s 25}^{\circ} s i n 65

Q. Evaluate:

sin 25^{\circ} cos 65^{\circ} + cos 25^{\circ} sin 65^{\circ}

Evaluate

$(i) \frac{{sin}^{2} 63^{\circ} + {sin}^{2} 27^{\circ}}{{cos}^{2} 17^{\circ} + {cos}^{2} 73^{\circ}}$

$(i i) sin 25^{\circ} cos 65^{\circ} + cos 25^{\circ} sin 65^{\circ}$

Q. Evaluate:
(i)

\frac{{sin}^{2} 63^{\circ} + {sin}^{2} 27^{\circ}}{{cos}^{2} 17^{\circ} + {cos}^{2} 73^{\circ}}

(ii)

sin 25^{\circ} cos 65^{\circ} + cos 25^{\circ} sin 65^{\circ}

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Sum of Trigonometric Ratios in Terms of Their Product

Standard XI Mathematics

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Question 3 (ii) Evaluate: (ii) sin25∘cos65∘+cos25∘sin65∘

(ii) sin25∘cos65∘+cos25∘sin65∘ =sin(90∘−65∘)cos65∘+cos(90∘−65∘)sin65∘ =cos65∘cos65∘+sin65∘sin65∘ =cos265∘+sin265∘=1

Question 3 (ii)
Evaluate:
(ii) $s i n 25^{\circ} c o s 65^{\circ} + c o s 25^{\circ} s i n 65^{\circ}$