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Without using trigonometric tables, prove that:(i) sin53° cos37° + cos53° sin37° = 1(ii) cos54° cos36° − sin54° sin36° = 0(iii) sec70° sin20° + cos20° cosec70° = 2(iv) tan 15° tan 60° tan 75° = 3(v) tan48° tan23° tan42° tan67° tan 45° = 1(vi) (sin72° + cos18°)(sin72° − cos18°) = 0(vii) cosec 39° cos 51° + tan 21° cot 69° – sec221° = 0

Answer» Without using trigonometric tables, prove that:

(i) sin53° cos37° + cos53° sin37° = 1

(ii) cos54° cos36° − sin54° sin36° = 0

(iii) sec70° sin20° + cos20° cosec70° = 2

(iv) tan 15° tan 60° tan 75° = 3

(v) tan48° tan23° tan42° tan67° tan 45° = 1

(vi) (sin72° + cos18°)(sin72° − cos18°) = 0

(vii) cosec 39° cos 51° + tan 21° cot 69° – sec221° = 0


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