Sin 25 ÷ cos 65 - Sin 65 ÷ cos 25
Answers
Answer- The above question is from the topic 'Trigonometric Ratios of Complementary Angles' of the chapter- Trigonometric Ratios'.
Here are the T-Ratios of complementary angles (angles whose sum is 90°):
1. sin(90°-θ)= cos θ
2. cos(90°-θ)= sin θ
3. tan(90°-θ)= cot θ
4. cosec(90°-θ)= sec θ
5. sec(90°-θ)= cosec θ
6. cot(90°-θ)= tan θ
We will be applying the 1. in this question.
Question: sin 25° ÷ cos 65° - sin 65° ÷ cos 25°
Solution:
1. Let us check if the above 2 angles i.e. 25° and 65° are complementary angles or not.
⇒ 25°+65° = 90°
∴ These are complementary angles.
2. Change only one T-Ratio.
In the above question, we will change sin 25° and sin 65°.
3. Obtain the values to be changed.
25°+65° = 90°
⇒ 25°= 90°-65°
⇒ 65°= 90°-25°
4. Substitute the values.
⇒ sin 25° ÷ cos 65° - sin 65° ÷ cos 25°
= [sin (90°-65°) ÷ cos 65°] - [sin (90°-25°) ÷ cos 25°]
= [cos 65° ÷ cos 65°] - [cos 25° ÷ cos 25°]
{∵ sin(90°-θ)= cos θ where θ= 65° and 25° respectively}
= 1 - 1
= 0
∴ sin 25° ÷ cos 65° - sin 65° ÷ cos 25°= 0
Answer:
here is your answer
The Answer is 0 because (cos 65°/cos 65° ) and (cos25°/ cos25°) cancel out
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