Sec 75° + sin 70° + tan 85° in terms of trigonometric ratios angles

1.	Sec 75° + sin 70° + tan 85° in terms of trigonometric ratios angles between 0° and 45°Cosec 15° + Cos 20° + Cot 5°Cosec 20° + Cos 15° + Cot 15°Cosec 5° + Cos 20° + Cot 15°Cosec 20° + Cos 5° + Cot 5°
Answer» Step-by-step EXPLANATION: (i) sin26°cos64° sin26°cos64°=sin90°-64°cos64° =cos64°cos64° ∵ sin90°-θ=cosθ =1Hence, sin26°cos64°=1 (ii) sec11∘cosec79∘ =SEC(90∘−79∘)cosec79∘ =cosec79∘cosec79∘ [∵sec 90-θ = cosec θ]=1 (III) tan65°cot25° tan65°cot25°=tan90°-25°cot25° =cot25°cot25° ∵ tan90°-θ=cotθ =1Hence, tan65°cot25°=1 (iv) cos37°sin53° cos37°sin53°=cos90°-53°sin53° =sin53°sin53° ∵ cos90°-θ=sinθ =1Hence, cos37°sin53°=1 (V)cosec42∘sec48∘ =cosec(90∘−48∘)sec48∘ =sec48∘sec48∘ [∵sec 90-θ = cosec θ] =1 (vi) cot34°tan56° cot34°tan56°=cot90°-56°tan56° =tan56°tan56° ∵ cot90°-θ=tanθ =1Hence, cot34°tan56°=1

Sec 75° + sin 70° + tan 85° in terms of trigonometric ratios angles between 0° and 45°Cosec 15° + Cos 20° + Cot 5°Cosec 20° + Cos 15° + Cot 15°Cosec 5° + Cos 20° + Cot 15°Cosec 20° + Cos 5° + Cot 5°

Answer»

Step-by-step EXPLANATION:

(i) sin26°cos64°

sin26°cos64°=sin90°-64°cos64° =cos64°cos64° ∵ sin90°-θ=cosθ =1Hence, sin26°cos64°=1

(ii) sec11∘cosec79∘ =SEC(90∘−79∘)cosec79∘ =cosec79∘cosec79∘ [∵sec 90-θ = cosec θ]=1

(III) tan65°cot25°

tan65°cot25°=tan90°-25°cot25° =cot25°cot25° ∵ tan90°-θ=cotθ =1Hence, tan65°cot25°=1

(iv) cos37°sin53°

cos37°sin53°=cos90°-53°sin53° =sin53°sin53° ∵ cos90°-θ=sinθ =1Hence, cos37°sin53°=1

(V)cosec42∘sec48∘ =cosec(90∘−48∘)sec48∘ =sec48∘sec48∘ [∵sec 90-θ = cosec θ] =1

(vi) cot34°tan56°

cot34°tan56°=cot90°-56°tan56° =tan56°tan56° ∵ cot90°-θ=tanθ =1Hence, cot34°tan56°=1

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