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 = _______.

(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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