Question

Evaluate
(i) tan 36º/cot 54º (ii) cos12º − sin78º (iii) cosec 31º − sec 59º
(iv) sin 15º sec 75º (vi) tan 26º tan64º

Answer 1

Evaluate
(i) tan 36º/cot 54º =1
(ii) cos12º − sin78º =0
(iii) cosec 31º − sec 59º =0
(iv) sin 15º sec 75º= 1
(vi) tan 26º tan64º= 1

Answer 2

Answer:

(i) 1, (ii) 0, (iii) 0, (iv) 1, (v) 1

Step-by-step explanation:

We have to evaluate the followings:

(i) tan 36°/Cot 54°= tan (90°-54°)/Cot 54° =Cot 54°/Cot 54° =1 (Answer)

{Since we know that, tan (90°-α)=Cot α}

(ii) Cos 12° - Sin 78° =Cos (90°-78°) - Sin 78°=Sin 78°- Sin 78° =0 (Answer)

{Since we know that, Cos (90°-α) = Sin α}

(iii) Cosec 31° - Sec 59° =Cosec (90°-59°) - Sec 59° =Sec 59°- Sec 59° =0 (Answer)

{Since we know that, Cosec (90°-α)= Sec α}

(iv) Sin 15° Sec 75° =Sin (90°-75°) . Sec 75° =Cos 75°. Sec 75° =1 (Answer)

{Since we know that, Sin (90°-α)=Cos α}

(v) tan 26°. tan 64° =tan (90°-64°). tan 64° = Cot 64°. Tan 64° =1 (Answer)

{Since we know that, tan (90°-α)=Cot α}