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Complementary angles

Solve the first problem 14 problems

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  1. Trig expression with complementary angles ●○○○○ 10 ptsWithout using trigonometric tables, evaluate cos⁡226∘+cos⁡64∘sin⁡26∘+tan⁡36∘cot⁡54∘\cos^2 26^\circ + \cos 64^\circ \sin 26^\circ + \dfrac{\tan 36^\circ}{\cot 54^\circ}.
  2. Trig expression with complementary angles ●○○○○ 10 ptsWithout using trigonometric tables, evaluate sin⁡234∘+sin⁡256∘+2tan⁡18∘tan⁡72∘−cot⁡230∘\sin^2 34^\circ + \sin^2 56^\circ + 2\tan 18^\circ \tan 72^\circ - \cot^2 30^\circ.
  3. Difference of squared sine and cosine ●○○○○ 10 ptsEvaluate (sin⁡72∘+cos⁡18∘)(sin⁡72∘−cos⁡18∘)(\sin 72^\circ + \cos 18^\circ)(\sin 72^\circ - \cos 18^\circ).
  4. Difference of cosines at 36 and 72 degrees ●●○○○ 20 ptsCompute cos⁡36∘−cos⁡72∘\cos 36^\circ - \cos 72^\circ. Give your answer as a decimal.
  5. Trigonometric identities with complementary angles ●●○○○ 20 ptsEvaluate (cos⁡225∘+cos⁡265∘)+csc⁡θsec⁡(90∘−θ)−cot⁡θtan⁡(90∘−θ)(\cos^2 25^\circ + \cos^2 65^\circ) + \csc\theta \sec(90^\circ - \theta) - \cot\theta \tan(90^\circ - \theta).
  6. Cosine of arcsecant plus arccosecant ●●○○○ 20 ptsEvaluate cos⁡(sec⁡−1x+csc⁡−1x)\cos\left(\sec^{-1}x+\csc^{-1}x\right) for ∣x∣≥1|x|\geq 1. (The answer is a single number, the same for every such xx.)

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