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191. Evaluate:

fraction numerator cos space 70 degree over denominator sin space 20 degree end fraction plus fraction numerator cos space 55 degree. space cosec space 35 degree over denominator tan space 65 degree. space tan space 25 degree end fraction minus tan space 45 degree. space tan space 5 degree. space tan space 85 degree.

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192. Evaluate:

fraction numerator 2 space sin space 68 degree over denominator cos space 22 degree end fraction minus fraction numerator 2 space cot space 15 degree over denominator 5 space tan space 75 degree end fraction minus fraction numerator 3 space tan space 45 degree. space tan space 20 degree. space tan space 40 degree. space tan space 50 degree. space tan space 70 degree over denominator 5 end fraction

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193.

Show that:
tan 20°. tan 35°. tan 45°. tan 55° tan 70° = 1

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194.

Show that:
sin 63°. cos 27° + cos 63°. sin 27° = 1

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195.

Show that:
sin 63°. cos 27° + cos 63°. sin 27° = 1

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Solution not provided.

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197.

Show that:
cos 38°. cos 52° - sin 38°. sin 52° = 0

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198.

Show that:
tan 48°. tan 23°. tan 42°. tan 67° = 1.

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199. If A and C are angles of a right angled triangle ABC right angled at B. Prove that
sin² A + sin² C = 1

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200. If A and C are angles of a right angled triangle ABC right angled at B. Prove that
1 + tan²A = cosec² C

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