Important Formulas and Questions
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Q1) If sec θ + tan θ = 2, what is the value of sec θ? 1) 3/2 2) 5/2 3) 2 4) 5/4 sec2θ - tan2θ = 1 (sec θ - tan θ)(sec θ + tan θ) = 1 sec θ - tan θ = 1/2 sec θ + tan θ = 2 (Given in the question) Adding the above 2 equations 2sec θ = 5/2 So, sec θ = 5/4 Hence, option 4. Q2) If sec θ - cosec θ = 0 then the value of tan θ + cot θ is 1) 0 2) 1 3) -1 4) 2 sec θ - cosec θ = 0 sin θ = cos θ tan θ = 1 tan θ + cot θ = tan θ + 1/tan θ = 1 + 1 = 2 Hence, option 4. Q3) If  then the value of  is1) 0 2) 1/3 3) 2/3 4) 4/3  Hence, option 3. Read More:Trigonometric Identities  is1) 0.5 2) -0.5 3) 3 4) -3  Hence, option 3. Q5) If sec2θ + tan2θ = 7/12 then sec4θ - tan4θ is equal to 1) 7/12 2) 1/2 3) 5/12 4) 1 sec4θ - tan4θ = (sec2θ + tan2θ)(sec2θ - tan2θ) = 7/12 Hence, option 1. Q6) The value of tan 1°.tan 2°.tan 3°---tan 89° 1) 0 2) 1 3) 89 4) undefined tan a . tan b = 1 where a + b = 90° tan 1°.tan 2°.tan 3°---tan 89° = 1 Hence, option 2. 1) A = 2B 2) 2A = B 3) -2A = B 4) A = -2B B = 2 cot 61°.cot 79° B = 2 cot(90 - 29)°cot(90 - 11)° B = 2 tan 11°.tan 29° B = 2A Hence, option 2. Q8) If α, β and γ are acute angled such that sin α = sqrt(3)/2 = cos β and tan γ = 1, then what is α + β + γ is equal to? 1) 105° 2) 120° 3) 135° 4) 150° sin α = sqrt(3)/2 i.e. α = 60° cos β = sqrt(3)/2 i.e. β = 30° tan γ = 1 i.e. γ = 45° α + β + γ = 60° + 30° + 45° = 135° Hence, option 3. Q9) If tan 7θ tan 2θ = 1, then the value of tan3θ is 1) sqrt(3) 2) -1/sqrt(3) 3) 1/sqrt(3) 4) -sqrt(3) tan 7θ tan 2θ = 1 tan 7θ = cot 2θ tan 7θ = tan(90° - 2θ) 7θ = 90° - 2θ 9θ = 90° θ = 10° tan 3θ = tan 30° = 1/sqrt(3) Hence, option 3. Q10) What is the value of sin A cos A tan A + cos A sin A cot A 1) sin2A + cos A 2) sin2A + tan2A 3) sin2A + cot2A 4) cosec2A - cot2A sin A cos A tan A + cos A sin A cot A = sin2A + cos2A = 1 cosec2A - cot2A Hence, option 4.
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