Q12 of 31 Page 316

Let us write whether the following statements are true of false:

(i) The value of cos54° and sin36° are equal.


(ii) The simplified value of (sin 12° - cos78°) is 1.

(i) The statement is true


⇒ cos54° = cos(90 - 36)°


= sin36°


[cos(90 - θ) = sinθ]


∴ the value of cos54° and sin36° has same values


(ii) The given statement is False


⇒ sin12° - cos78°


⇒ sin12° - cos(90 - 12)°


⇒ sin12° - sin12°


= 0


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