Question

(Tan 32°-1) ( tan 77° +1) = ?? . step by step ans

Answer 1

Answer:

Question

12. (tan⁡32 −1)(tan⁡77∘+1)

Answer

(sin⁡(32)−cos⁡(32))sin⁡(77∘)+(sin⁡(32)−cos⁡(32))cos⁡(77∘)cos⁡(32)cos⁡(77∘)

Explanation

Apply Multiplicative Distribution Law: tan⁡(32)×(tan⁡(77∘)+1)−(tan⁡(77∘)+1)

Remove the parentheses: tan⁡(32)×(tan⁡(77∘)+1)−tan⁡(77∘)−1

Apply Multiplicative Distribution Law: tan⁡(32)tan⁡(77∘)+tan⁡(32)−tan⁡(77∘)−1

Combine like terms: (tan⁡(32)−1)tan⁡(77∘)+tan⁡(32)−1

Transform the expression using the quotient identity: (sin⁡(32)cos⁡(32)−1)tan⁡(77∘)+tan⁡(32)−1

Find common denominator and write the numerators above common denominator: sin⁡(32)−cos⁡(32)cos⁡(32)tan⁡(77∘)+tan⁡(32)−1

Transform the expression using the quotient identity: sin⁡(32)−cos⁡(32)cos⁡(32)⋅sin⁡(77∘)cos⁡(77∘)+sin⁡(32)cos⁡(32)−1

Write as a single fraction : (sin⁡(32)−cos⁡(32))sin⁡(77∘)cos⁡(32)cos⁡(77∘)+sin⁡(32)cos⁡(32)−1

Find common denominator and write the numerators above common denominator: (sin⁡(32)−cos⁡(32))sin⁡(77∘)+sin⁡(32)cos⁡(77∘)−cos⁡(32)cos⁡(77∘)cos⁡(32)cos⁡(77∘)

Combine like terms: (sin⁡(32)−cos⁡(32))sin⁡(77∘)+(sin⁡(32)−cos⁡(32))cos⁡(77∘)cos⁡(32)cos⁡(77∘)