MHT CET · Maths · Trigonometric Ratios & Identities
If \(a=\sin 175^{\circ}+\cos 175^{\circ}\), then
- A \(a>0\)
- B \(a=0\)
- C \(a < 0\)
- D \(a=1\)
Answer & Solution
Correct Answer
(C) \(a < 0\)
Step-by-step Solution
Detailed explanation
(B)
\(\begin{aligned} a &=\sin \left(180^{\circ}-5^{\circ}\right)+\cos \left(180^{\circ}-5^{\circ}\right) \\ &=\sin 5^{\circ}-\cos 5^{\circ} \end{aligned}\)
In first quadrunt, \(\sin \theta < \sin \theta < \cos \theta\)
When \(0 \leq \theta < 45^{\circ}\)
\(\therefore \sin 5^{\circ} < \cos 5^{\circ} \Rightarrow \sin 5^{\circ}-\cos 5^{\circ} < 0 \Rightarrow a < 0\)
\(\begin{aligned} a &=\sin \left(180^{\circ}-5^{\circ}\right)+\cos \left(180^{\circ}-5^{\circ}\right) \\ &=\sin 5^{\circ}-\cos 5^{\circ} \end{aligned}\)
In first quadrunt, \(\sin \theta < \sin \theta < \cos \theta\)
When \(0 \leq \theta < 45^{\circ}\)
\(\therefore \sin 5^{\circ} < \cos 5^{\circ} \Rightarrow \sin 5^{\circ}-\cos 5^{\circ} < 0 \Rightarrow a < 0\)
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