Chapter 8: Q.5 (page 553)

Find an exact value of each expression, without using a calculator $\cos^{2} 40 + \cos^{2} 50$

Short Answer

Expert verified

The simplified value is $1$

Step by step solution

Step 1. Given information

The given expression is $\cos^{2} 40 + \cos^{2} 50$

Step 2. Convert into the same trigonometrical ratio

The given expression is $\cos^{2} 40 + \cos^{2} 50$

Here. $\cos (90 - θ) = \sin θ$

Now $= \cos^{2} 40 + \cos^{2} 50 = \cos^{2} (90 - 50) + \cos^{2} 50 = \sin^{2} 50 + \cos^{2} 50 = 1$ Where $\sin^{2} θ + \cos^{2} θ = 1$

Step 3. Conclusion

Hence, the simplified value is $1$

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Find an exact value of each expression, without using a calculator $\cos^{2} 40 + \cos^{2} 50$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Convert into the same trigonometrical ratio

Step 3. Conclusion

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Find an exact value of each expression, without using a calculatorcos240+cos250

Short Answer

Step by step solution

Step 1. Given information

Step 2. Convert into the same trigonometrical ratio

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Calculus

Study anywhere. Anytime. Across all devices.

Find an exact value of each expression, without using a calculator $\cos^{2} 40 + \cos^{2} 50$