Find the value of $\frac{\cos 35^\circ}{\sin 55^\circ} - \frac{\sin 11^\circ}{\cos 79^\circ} + \cos 28^\circ \csc 62^\circ + \cos 0^\circ $.

The correct answer is Option C: 2. Use complementary angles (90° - θ) to convert terms to 1. Since cos 35° = sin 55° and sin 11° = cos 79°, the expression simplifies to 1 - 1 + 1 + 1 = 2. Step-by-Step Solution & Concepts: Shortcut Trick: Use complementary angles (90° - θ) to convert terms to 1. Since cos 35° = sin 55° and sin 11° = cos 79°, the expression simplifies to 1 - 1 + 1 + 1 = 2. Formula Used: $$\cos(90^\circ - \theta) = \sin\theta, \sin(90^\circ - \theta) = \cos\theta, \csc\theta = \frac{1}{\sin\theta}, \cos 0^\circ = 1$$ Given: Expression to evaluate: (cos 35° / sin 55°) - (sin 11° / cos 79°) + (cos 28° * cosec 62°) + cos 0° Steps: Convert first two terms using complementary angles: Apply the identity $\cos(90^\circ - \theta) = \sin \theta$. Thus, $\cos 35^\circ = \sin(90^\circ - 35^\circ) = \sin 55^\circ$ and $\sin 11^circ = \cos(90^\circ - 11^circ) = \cos 79^\circ$.. Simplify the third term: Convert $\csc 62^\circ$ to $1 / \sin 62^\circ$. Since $62^\circ = 90^\circ - 28^\circ$, we have $\sin 62^\circ = \cos 28^\circ$. Thus, $\cos 28^\circ \times (1 / \cos 28^\circ) = 1$.. Calculate the final sum: Substitute the simplified parts and include $\cos 0^\circ = 1$: $0 + 1 + 1 = 2$. Answer: C is correct because the expression simplifies to 1 - 1 + 1 + 1, which equals 2. Exam Tip: These identities appear frequently in height and distance problems to simplify complex ratios quickly.

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MathematicsPrevious Year Paper 2024

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Find the value of $\frac{\cos 35°{\sin 55° - \frac{\sin 11°{\cos 79° + \cos 28°\csc 62°+ \cos 0°$ .

Correct Answer

📐 MA • Math Direct FormulaMathematicsPrevious Year Paper 2024

Option C

Quick Summary:

Use complementary angles (90° - θ) to convert terms to 1. Since cos 35° = sin 55° and sin 11° = cos 79°, the expression simplifies to 1 - 1 + 1 + 1 = 2.

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📐MAMath SolutionDirect Formula

📋 Given

Expression to evaluate: (cos 35° / sin 55°) - (sin 11° / cos 79°) + (cos 28° * cosec 62°) + cos 0°

🔢 Formula Used

cos⁡(90°−θ)=sin⁡θ,sin⁡(90°−θ)=cos⁡θ,csc⁡θ=1sin⁡θ,cos⁡0°=1\cos(90°- \theta) = \sin\theta, \sin(90°- \theta) = \cos\theta, \csc\theta = \frac{1}{\sin\theta}, \cos 0°= 1cos(90°−θ)=sinθ,sin(90°−θ)=cosθ,cscθ=sinθ1​,cos0°=1

⚡ Exam Hall Shortcut / Speed Trick

Use complementary angles (90° - θ) to convert terms to 1. Since cos 35° = sin 55° and sin 11° = cos 79°, the expression simplifies to 1 - 1 + 1 + 1 = 2.

⚠️ Common Student Trap / Pitfall

Many students mistake cos 0° for 0 instead of 1, leading to an incorrect result of 1.

🔢 Step-by-Step Solution

Convert first two terms using complementary angles

Apply the identity $\cos(90°- \theta) = \sin \theta$ . Thus, $\cos 35°= \sin(90°- 35°) = \sin 55°$ and $\sin 11^circ = \cos(90°- 11^circ) = \cos 79°$ .

\frac{\sin 55°{\sin 55° - \frac{\cos 79°{\cos 79° = 1 - 1 = 0

Simplify the third term

Convert $\csc 62°$ to $1 / \sin 62°$ . Since $62°= 90°- 28°$ , we have $\sin 62°= \cos 28°$ . Thus, $\cos 28°\times (1 / \cos 28°) = 1$ .

\cos 28°\cdot \csc 62°= \cos 28°\cdot \frac{1}{\cos 28° = 1

Calculate the final sum

Substitute the simplified parts and include $\cos 0°= 1$ : $0 + 1 + 1 = 2$ .

0+1+1=20 + 1 + 1 = 20+1+1=2

✅

C is correct because the expression simplifies to 1 - 1 + 1 + 1, which equals 2.

Core Concepts Used

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Complementary Angle Identities Trigonometric Reciprocal Identities Standard Trigonometric Values

💡 EXAM TIP

These identities appear frequently in height and distance problems to simplify complex ratios quickly.

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