c) \( 3 \operatorname{sen}^{2} x-9 \operatorname{sen} x \cdot \operatorname{ctg} x+7 \cos ^{2} x-4 \cos x=(4 \cos x-1)(\cos x-3) \) d) \( \sqrt{\frac{1-\cos \beta}{1+\cos \beta}}+\sqrt{\frac{1+\cos \beta}{1-\cos \beta}}=2 \csc \beta \)
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Mind Expander
Did you know that equations involving trigonometric functions like sine and cosine have been studied for centuries? The ancient Greeks and later mathematicians used these functions extensively in astronomy and navigation, laying the groundwork for calculus and analytical geometry. Their discoveries help us solve not only mathematical puzzles but also practical problems, from constructing buildings to plotting space missions! If you're diving into trigonometric identities and equations, a common pitfall is misapplying fundamental identities, like the Pythagorean identity or forgetting about the domain restrictions of functions. Always double-check your transformations and consider angle values carefully! A little mindfulness can go a long way in avoiding errors and deepening your understanding of trigonometric relationships.