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EXERCISE 2.277787586360Q.1 Prove?To prove:?Let?x?= sinθ. Then,?We have,R.H.S. == 3θ= L.H.S.75438092710Q.2 Prove?To prove:Let?x?= cosθ. Then, cos?1?x?=θ.We have,127127012065Q.3 Prove?To prove:1080135-1905lefttopQ.4 Prove?To prove:?26466804392930Q.5 Write the function in the simplest form:Q.6 Write the function in the simplest form:Put?x?= cosec?θ???θ?= cosec?1?x275780537465Q. 7 Write the function in the simplest form:27736802624455Q.8 Write the function in the simplest form:lefttop2750185356235Q.9 Write the function in the simplest form:27578052361565Q.10 Write the function in the simplest form:15735303251835Q.11 Find the value of?Let. Then,1485900-1905Q.12 Find the value of?1470025812165Q.13 Find the value of?Let?x?= tan?θ. Then,?θ?= tan?1?x.Let?y?= tan?Φ. Then,?Φ?= tan?1?y.610870212725Q.14 If, then find the value of?x.19869154467860Q.15 If, then find the value of?x.1517650-1905Q.16 Find the values of?We know that sin?1?(sin?x) =?x?if, which is the principal value branch of sin?1x.Here,Now,?can be written as:147002574295Q.17 Find the values ofWe know that tan?1?(tan?x) =?x?if, which is the principal value branch of tan?1x.Here,Now,?can be written as:151765078105Q.18 Find the values of?Let. Then,Q.19 Find the values of?is equal to(A) (B) (C) (D) We know that cos?1?(cos?x) =?x?if, which is the principal value branch of cos??1x.Here,Now,?can be written as:The correct answer is B.Q.20 Find the values of?is equal to (A) (B) (C) (D) 1Let. Then,?We know that the range of the principal value branch of.∴The correct answer is D.Q.21 Find the values of?is equal to (A) π (B) (C) 0 (D) et. Then,We know that the range of the principal value branch ofLet.The range of the principal value branch ofThe correct answer is B. ................
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