Q. 12 C4.0( 5 Votes )

Let us fill up the blanks:

(i) The value of (tan 15° x tan 45° x tan 60° tan 75°) is_______.

(ii) The value of (sin 12° x cos 18° x sec 78° cosec 72°) is _______.

(iii) If A and B are complementary to each other, siin A = _______.

Answer :

(i) The value of tan15° tan45° tan60° tan75° is √3


we know that tan45° = 1 and tan60° = √3


tan15°(1)(√3)tan(90 - 15)


√3 × tan15° cot15°


√3 × tan15°


= √3 × 1


= √3


(ii) The value of sin12°cos18° × sec78°cosec72° is 1


sin12°cos18° sec78°cosec72°


sin12°cos18°sec(90 - 12)°cosec(90 - 18)°


sin12°cos18°cosec12°sec18°


sin12°cos18°


= 1


(iii) sinA = cosB


If A and B are complementary angles then A + B = 90° and A = 90 - B


sinA = sin(90 - B)


= cosB


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